arXiv subjects

Peter Schneider

Publications and source records attributed to Peter Schneider.

At least 91 records · Page 5Linked to original sources

arXiv2016

HIFLUGCS: X-ray luminosity -- dynamical mass relation and its implications for mass calibrations with the SPIDERS and 4MOST surveys

We present the X-ray luminosity (L) versus dynamical mass (M) relation for 63 nearby clusters in the HIFLUGCS. The luminosity measurements are obtained based on ~1.3 Ms of clean XMM data and ROSAT pointed observations. The masses are estimated using optical spectroscopic redshifts of 13647 cluster galaxies in total. Given sufficient numbers of member galaxies in computing the dynamical masses, the L-M relations agree between the disturbed and undisturbed clusters. The cool-core clusters still dominate the scatter in the L-M relation even when a core corrected X-ray luminosity is used, which indicates that the scatter mainly reflects the structure formation history of the clusters. As shown by the clusters with a small number of redshifts, the dynamical masses can be underestimated leading to a biased scaling relation. To investigate the potential of spectroscopic surveys to follow up high-redshift galaxy clusters/groups observed in X-ray surveys for the identifications and mass calibrations, we carried out Monte-Carlo re-sampling of the cluster galaxy redshifts and calibrated the uncertainties of the redshift and dynamical mass estimates when only reduced numbers of galaxy redshifts per cluster are available. The re-sampling considers the SPIDERS and 4MOST configurations, designed for the follow-up of the eROSITA clusters, and was carried out for each cluster at the actual cluster redshift as well as at z=0.2, 0.4, 0.6, and 0.8. For following up very distant cluster/groups, we carried out the mass calibration based on the re-sampling with only 10zs/cluster, and redshift calibration based on the re-sampling with only 5zs/cluster and 10zs/cluster, respectively. Our results demonstrate the power of combining upcoming X-ray and optical spectroscopic surveys for mass calibration. The scatter in the dynamical mass estimates for the clusters with at least ten members is within 50%.

astro-ph.CO↗

arXiv2016

Ambiguities in gravitational lens models: the density field from the source position transformation

Strong gravitational lensing is regarded as the most precise technique to measure the mass in the inner region of galaxies or galaxy clusters. In particular, the mass within one Einstein radius can be determined with an accuracy of order of a few percent or better, depending on the image configuration. For other radii, however, degeneracies exist between galaxy density profiles, precluding an accurate determination of the enclosed mass. The source position transformation (SPT), which includes the well-known mass-sheet transformation (MST) as a special case, describes this degeneracy of the lensing observables in a more general way. In this paper we explore properties of an SPT, removing the MST to leading order, i.e., we consider degeneracies which have not been described before. The deflection field $\boldsymbol{\hatα}(\boldsymbolθ)$ resulting from an SPT is not curl-free in general, and thus not a deflection that can be obtained from a lensing mass distribution. Starting from a variational principle, we construct lensing potentials that give rise to a deflection field $\boldsymbol{\tildeα}$, which differs from $\boldsymbol{\hatα}$ by less than an observationally motivated upper limit. The corresponding mass distributions from these 'valid' SPTs are studied: their radial profiles are modified relative to the original mass distribution in a significant and non-trivial way, and originally axi-symmetric mass distributions can obtain a finite ellipticity. These results indicate a significant effect of the SPT on quantitative analyses of lens systems. We show that the mass inside the Einstein radius of the original mass distribution is conserved by the SPT; hence, as is the case for the MST, the SPT does not affect the mass determination at the Einstein radius. [...]

astro-ph.CO↗

arXiv2016

Dependence of GAMA galaxy halo masses on the cosmic web environment from 100 square degrees of KiDS weak lensing data

Galaxies and their dark matter haloes are part of a complex network of mass structures, collectively called the cosmic web. Using the tidal tensor prescription these structures can be classified into four cosmic environments: voids, sheets, filaments and knots. As the cosmic web may influence the formation and evolution of dark matter haloes and the galaxies they host, we aim to study the effect of these cosmic environments on the average mass of galactic haloes. To this end we measure the galaxy-galaxy lensing profile of 91,195 galaxies, within 0.039 < z < 0.263, from the spectroscopic Galaxy And Mass Assembly (GAMA) survey, using ~100 square degrees of overlapping data from the Kilo-Degree Survey (KiDS). In each of the four cosmic environments we model the contributions from group centrals, satellites and neighbouring groups to the stacked galaxy-galaxy lensing profiles. After correcting the lens samples for differences in the stellar mass distribution, we find no dependence of the average halo mass of central galaxies on their cosmic environment. We do find a significant increase in the average contribution of neighbouring groups to the lensing profile in increasingly dense cosmic environments. We show, however, that the observed effect can be entirely attributed to the galaxy density at much smaller scales (within 4 Mpc/h), which is correlated with the density of the cosmic environments. Within our current uncertainties we find no direct dependence of galaxy halo mass on their cosmic environment.

astro-ph.GA↗

arXiv2016

Generalized shear-ratio tests: A new relation between cosmological distances, and a diagnostic for a redshift-dependent multiplicative bias in shear measurements

We derive a new relation between cosological distances, valid in any (statistically) isotropic space-time and independent of cosmological parameters or even the validity of the field equation of General Relativity. In particular, this relation yields an equation between those distance ratios which are the geometrical factors determining the strength of the gravitational lensing effect of mass concentrations. Considering a combination of weak lensing shear ratios, based on lenses at two different redshifts, and sources at three different redshifts, we derive a relation between shear-ratio tests which must be identically satisfied. A redshift-dependent multiplicative bias in shear estimates will violate this relation, and thus can be probed by this generalized shear-ratio test. Combining the lensing effect for lenses at three different redshifts and three different source redshifts, a relation between shear ratios is derived which must be valid independent of a multiplicative bias. We propose these generalized shear-ratio tests as a diagnostic for the presence of systematics in upcoming weak lensing surveys.

astro-ph.CO↗

arXiv2015

Coates-Wiles homomorphisms and Iwasawa cohomology for Lubin-Tate extensions

For the $p$-cyclotomic tower of $\mathbb{Q}_p$ Fontaine established a description of local Iwasawa cohomology with coefficients in a local Galois representation $V$ in terms of the $ψ$-operator acting on the attached etale $(φ,Γ)$-module $D(V)$. In this article we generalize Fontaine's result to the case of arbitratry Lubin-Tate towers $L_\infty$ over finite extensions $L$ of $\mathbb{Q}_p$ by using the Kisin-Ren/Fontaine equivalence of categories between Galois representations and $(φ_L,Γ_L)$-module and extending parts of [Herr L.: Sur la cohomologie galoisienne des corps $p$-adiques. Bull. Soc. Math. France 126, 563-600 (1998)], [Scholl A. J.: Higher fields of norms and $(ϕ,Γ)$-modules. Documenta Math.\ 2006, Extra Vol., 685-709]. Moreover, we prove a kind of explicit reciprocity law which calculates the Kummer map over $L_\infty$ for the multiplicative group twisted with the dual of the Tate module $T$ of the Lubin-Tate formal group in terms of Coleman power series and the attached $(φ_L,Γ_L)$-module. The proof is based on a generalized Schmid-Witt residue formula. Finally, we extend the explicit reciprocity law of Bloch and Kato [Bloch S., Kato K.: $L$-functions and Tamagawa numbers of motives. The Grothendieck Festschrift, Vol. I, 333-400, Progress Math., 86, Birkhäuser Boston 1990] Thm. 2.1 to our situation expressing the Bloch-Kato exponential map for $L(χ_{LT}^r)$ in terms of generalized Coates-Wiles homomorphisms, where the Lubin-Tate characater $χ_{LT}$ describes the Galois action on $T.$

math.NT↗

arXiv2015

Rigid character groups, Lubin-Tate theory, and $(φ,Γ)$-modules

The construction of the $p$-adic local Langlands correspondence for $\mathrm{GL}_2(\mathbf{Q}_p)$ uses in an essential way Fontaine's theory of cyclotomic $(φ,Γ)$-modules. Here \emph{cyclotomic} means that $Γ= \mathrm{Gal}(\mathbf{Q}_p(μ_{p^\infty})/\mathbf{Q}_p)$ is the Galois group of the cyclotomic extension of $\mathbf{Q}_p$. In order to generalize the $p$-adic local Langlands correspondence to $\mathrm{GL}_2(L)$, where $L$ is a finite extension of $\mathbf{Q}_p$, it seems necessary to have at our disposal a theory of Lubin-Tate $(φ,Γ)$-modules. Such a generalization has been carried out to some extent, by working over the $p$-adic open unit disk, endowed with the action of the endomorphisms of a Lubin-Tate group. The main idea of our article is to carry out a Lubin-Tate generalization of the theory of cyclotomic $(φ,Γ)$-modules in a different fashion. Instead of the $p$-adic open unit disk, we work over a character variety, that parameterizes the locally $L$-analytic characters on $o_L$. We study $(φ,Γ)$-modules in this setting, and relate some of them to what was known previously.

math.NT↗

arXiv2015

Constrained correlation functions from the Millennium Simulation

Context. In previous work, we developed a quasi-Gaussian approximation for the likelihood of correlation functions, which, in contrast to the usual Gaussian approach, incorporates fundamental mathematical constraints on correlation functions. The analytical computation of these constraints is only feasible in the case of correlation functions of one-dimensional random fields. Aims. In this work, we aim to obtain corresponding constraints in the case of higher-dimensional random fields and test them in a more realistic context. Methods. We develop numerical methods to compute the constraints on correlation functions which are also applicable for two- and three-dimensional fields. In order to test the accuracy of the numerically obtained constraints, we compare them to the analytical results for the one-dimensional case. Finally, we compute correlation functions from the halo catalog of the Millennium Simulation, check whether they obey the constraints, and examine the performance of the transformation used in the construction of the quasi-Gaussian likelihood. Results. We find that our numerical methods of computing the constraints are robust and that the correlation functions measured from the Millennium Simulation obey them. Despite the fact that the measured correlation functions lie well inside the allowed region of parameter space, i.e. far away from the boundaries of the allowed volume defined by the constraints, we find strong indications that the quasi-Gaussian likelihood yields a substantially more accurate description than the Gaussian one.

astro-ph.CO↗

arXiv2015

Gravitational Lensing Analysis of the Kilo Degree Survey

The Kilo-Degree Survey (KiDS) is a multi-band imaging survey designed for cosmological studies from weak lensing and photometric redshifts. It uses the ESO VLT Survey Telescope with its wide-field camera OmegaCAM. KiDS images are taken in four filters similar to the SDSS ugri bands. The best-seeing time is reserved for deep r-band observations that reach a median 5-sigma limiting AB magnitude of 24.9 with a median seeing that is better than 0.7arcsec. Initial KiDS observations have concentrated on the GAMA regions near the celestial equator, where extensive, highly complete redshift catalogues are available. A total of 109 survey tiles, one square degree each, form the basis of the first set of lensing analyses, which focus on measurements of halo properties of GAMA galaxies. 9 galaxies per square arcminute enter the lensing analysis, for an effective inverse shear variance of 69 per square arcminute. Accounting for the shape measurement weight, the median redshift of the sources is 0.53. KiDS data processing follows two parallel tracks, one optimized for galaxy shape measurement (for weak lensing), and one for accurate matched-aperture photometry in four bands (for photometric redshifts). This technical paper describes how the lensing and photometric redshift catalogues have been produced (including an extensive description of the Gaussian Aperture and Photometry pipeline), summarizes the data quality, and presents extensive tests for systematic errors that might affect the lensing analyses. We also provide first demonstrations of the suitability of the data for cosmological measurements, and explain how the shear catalogues were blinded to prevent confirmation bias in the scientific analyses. The KiDS shear and photometric redshift catalogues, presented in this paper, are released to the community through http://kids.strw.leidenuniv.nl .

astro-ph.CO↗

arXiv2015

The masses of satellites in GAMA galaxy groups from 100 square degrees of KiDS weak lensing data

We use the first 100 sq. deg. of overlap between the Kilo-Degree Survey (KiDS) and the Galaxy And Mass Assembly (GAMA) survey to determine the galaxy halo mass of ~10,000 spectroscopically-confirmed satellite galaxies in massive ($M > 10^{13}h^{-1}{\rm M}_\odot$) galaxy groups. Separating the sample as a function of projected distance to the group centre, we jointly model the satellites and their host groups with Navarro-Frenk-White (NFW) density profiles, fully accounting for the data covariance. The probed satellite galaxies in these groups have total masses $\log M_{\rm sub} /(h^{-1}{\rm M}_\odot) \approx 11.7 - 12.2$ consistent across group-centric distance within the errorbars. Given their typical stellar masses, $\log M_{\rm \star,sat}/(h^{-2}{\rm M}_\odot) \sim 10.5$, such total masses imply stellar mass fractions of $M_{\rm \star,sat} /M_{\rm sub} \approx 0.04 h^{-1}$ . The average subhalo hosting these satellite galaxies has a mass $M_{\rm sub} \sim 0.015M_{\rm host}$ independent of host halo mass, in broad agreement with the expectations of structure formation in a $Λ$CDM universe.

astro-ph.CO↗

arXiv2015

The first and second data releases of the Kilo-Degree Survey

The Kilo-Degree Survey (KiDS) is an optical wide-field imaging survey carried out with the VLT Survey Telescope and the OmegaCAM camera. KiDS will image 1500 square degrees in four filters (ugri), and together with its near-infrared counterpart VIKING will produce deep photometry in nine bands. Designed for weak lensing shape and photometric redshift measurements, the core science driver of the survey is mapping the large-scale matter distribution in the Universe back to a redshift of ~0.5. Secondary science cases are manifold, covering topics such as galaxy evolution, Milky Way structure, and the detection of high-redshift clusters and quasars. KiDS is an ESO Public Survey and dedicated to serving the astronomical community with high-quality data products derived from the survey data, as well as with calibration data. Public data releases will be made on a yearly basis, the first two of which are presented here. For a total of 148 survey tiles (~160 sq.deg.) astrometrically and photometrically calibrated, coadded ugri images have been released, accompanied by weight maps, masks, source lists, and a multi-band source catalog. A dedicated pipeline and data management system based on the Astro-WISE software system, combined with newly developed masking and source classification software, is used for the data production of the data products described here. The achieved data quality and early science projects based on the data products in the first two data releases are reviewed in order to validate the survey data. Early scientific results include the detection of nine high-z QSOs, fifteen candidate strong gravitational lenses, high-quality photometric redshifts and galaxy structural parameters for hundreds of thousands of galaxies. (Abridged)

astro-ph.CO↗

arXiv2015

How well can cold-dark-matter substructures account for the observed radio flux-ratio anomalies?

Discrepancies between the observed and model-predicted radio flux ratios are seen in a number of quadruply-lensed quasars. The most favored interpretation of these anomalies is that CDM substructures present in lensing galaxies perturb the lens potentials and alter image magnifications and thus flux ratios. So far no consensus has emerged regarding whether or not the predicted CDM substructure abundance fully accounts for the lensing flux anomaly observations. Accurate modeling relies on a realistic lens sample in terms of both the lens environment and internal structures and substructures. In this paper we construct samples of generalised and specific lens potentials, to which we add (rescaled) subhalo populations from the galaxy-scale Aquarius and the cluster-scale Phoenix simulation suites. We further investigate the lensing effects from subhalos of masses several orders of magnitude below the simulation resolution limit. The resulting flux ratio distributions are compared to the currently best available sample of radio lenses. The observed anomalies in B0128+437, B0712+472 and B1555+375 are more likely to be caused by propagation effects or oversimplified lens modeling, signs of which are already seen in the data. Among the quadruple systems that have closely located image triplets/pairs, the anomalous flux ratios of MG0414+0534 can be reproduced by adding CDM subhalos to its macroscopic lens potential, with a probability of 5%-20%; for B0712+472, B1422+231, B1555+375 and B2045+265, these probabilities are only of a few percent. We hence find that CDM substructures are unlikely to be the whole reason for radio flux anomalies. We discuss other possible effects that might also be at work.

astro-ph.CO↗

arXiv2014

How well can cold-dark-matter substructures account for the observed lensing flux-ratio anomalies?

Lensing flux-ratio anomalies are most likely caused by gravitational lensing by small-scale dark matter structures. These anomalies offer the prospect of testing a fundamental prediction of the cold dark matter (CDM) cosmological model: the existence of numerous substructures that are too small to host visible galaxies. In two previous studies we found that the number of subhalos in the six high-resolution simulations of CDM galactic halos of the Aquarius project is not sufficient to account for the observed frequency of flux ratio anomalies seen in selected quasars from the CLASS survey. These studies were limited by the small number of halos used, their narrow range of masses (1-2E12 solar masses) and the small range of lens ellipticities considered. We address these shortcomings by investigating the lensing properties of a large sample of halos with a wide range of masses in two sets of high resolution simulations of cosmological volumes and comparing them to a currently best available sample of radio quasars. We find that, as expected, substructures do not change the flux-ratio probability distribution of image pairs and triples with large separations, but they have a significant effect on the distribution at small separations. For such systems, CDM substructures can account for a substantial fraction of the observed flux-ratio anomalies. For large close-pair separation systems, the discrepancies existing between the observed flux ratios and predictions from smooth halo models are attributed to simplifications inherent in these models which do not take account of fine details in the lens mass distributions.

astro-ph.CO↗

arXiv2014

Can one determine cosmological parameters from multi-plane strong lens systems?

Strong gravitational lensing of sources with different redshifts has been used to determine cosmological distance ratios, which in turn depend on the expansion history. Hence, such systems are viewed as potential tools for constraining cosmological parameters. Here we show that in lens systems with two distinct source redshifts, of which the nearest one contributes to the light deflection towards the more distant one, there exists an invariance transformation which leaves all strong lensing observables unchanged (except the product of time delay and Hubble constant), generalizing the well-known mass-sheet transformation in single plane lens systems. The transformation preserves the relative distribution of mass and light, so that a `mass-follows-light' assumption does not fix the MST. All time delays (from sources on both planes) scale with the same factor -- time-delay ratios are therefore invariant under the MST. Changing cosmological parameters, and thus distance ratios, is essentially equivalent to such a mass-sheet transformation. As an example, we discuss the double source plane system SDSSJ0946+1006, which has been recently studied by Collett and Auger, and show that variations of cosmological parameters within reasonable ranges lead to only a small mass-sheet transformation in both lens planes. Hence, the ability to extract cosmological information from such systems depends heavily on the ability to break the mass-sheet degeneracy.

astro-ph.CO↗

arXiv2014

A New Data Compression Method and its Application to Cosmic Shear Analysis

Future large scale cosmological surveys will provide huge data sets whose analysis requires efficient data compression. Calculating accurate covariances is extremely challenging with increasing number of statistics used. Here we introduce a formalism for achieving efficient data compression, based on a local expansion of statistical measures around a fiducial cosmological model. We specifically apply and test this approach for the case of cosmic shear statistics. We demonstrate the performance of our approach, using a Fisher analysis on cosmic shear tomography described in terms of E-/B-mode separating statistics (COSEBIs). We show that our data compression is highly effective in extracting essentially the full cosmological information from a strongly reduced number of observables. Specifically, the number of statistics needed decreases by at least one order of magnitude relative to the COSEBIs, which already compress the data substantially compared to the shear two-point correlation functions. The efficiency appears to be affected only slightly if a highly inaccurate covariance is used for defining the compressed statistics, showing the robustness of the method. We conclude that an efficient data compression is achievable and that the number of compressed statistics depends on the number of model parameters. In addition, we study how well band powers can be obtained from measuring shear correlation functions over a finite interval of separations. We show the strong limitations on the possibility to construct top-hat filters in Fourier space, for which the real-space analog has a finite support, yielding strong bounds on the accuracy of band power estimates. The error on an estimated band-power is larger for a narrower filter and a smaller angular range which for relevant cases can be as large as 10%.

astro-ph.CO↗

arXiv2014

Generalized multi-plane gravitational lensing: time delays, recursive lens equation, and the mass-sheet transformation

We consider several aspects of the generalized multi-plane gravitational lens theory, in which light rays from a distant source are affected by several main deflectors, and in addition by the tidal gravitational field of the large-scale matter distribution in the Universe when propagating between the main deflectors. Specifically, we derive a simple expression for the time-delay function in this case, making use of the general formalism for treating light propagation in inhomogeneous spacetimes which leads to the characterization of distance matrices between main lens planes. Applying Fermat's principle, an alternative form of the corresponding lens equation is derived, which connects the impact vectors in three consecutive main lens planes, and we show that this form of the lens equation is equivalent to the more standard one. For this, some general relations for cosmological distance matrices are derived. The generalized multi-plane lens situation admits a generalized mass-sheet transformation, which corresponds to uniform isotropic scaling in each lens plane, a corresponding scaling of the deflection angle, and the addition of a tidal matrix (mass sheet plus external shear) to each main lens. We show that the time delay for sources in all lens planes scale with the same factor under this generalized mass-sheet transformation, thus precluding the use of time-delay ratios to break the mass-sheet transformation.

astro-ph.CO↗

arXiv2014

Combining Probes of Large-Scale Structure with CosmoLike

Developing accurate analysis techniques to combine various probes of cosmology is essential to tighten constraints on cosmological parameters and to check for inconsistencies in our model of the Universe. In this paper we develop a joint analysis framework for six different second-order statistics calculated from three tracers of the dark matter density field, namely galaxy position, shear, and magnification. We extend a data compression scheme developed in the context of shear-shear statistics (the so-called COSEBIs) to the other five second-order statistics, thereby significantly reducing the number of data points in the joint data vector. We use CosmoLike, a newly developed software framework for joint likelihood analyses, to forecast parameter constraints for the Dark Energy Survey (DES). The simulated MCMCs cover a five dimensional cosmological parameter space comparing the information content of the individual probes to several combined probes (CP) data vectors. Given the significant correlations of these second-order statistics we model all cross terms in the covariance matrix; furthermore we go beyond the Gaussian covariance approximation and use the halo model to include higher order correlations of the density field. We find that adding magnification information (including cross probes with shear and clustering) noticeably increases the information content and that the correct modeling of the covariance (i.e., accounting for non-Gaussianity and cross terms) is essential for accurate likelihood contours from the CP data vector. We also identify several nulltests based on the degeneracy of magnification and shear statistics which can be used to quantify the contamination of data sets by astrophysical systematics and/or calibration issues.

astro-ph.CO↗

arXiv2014

The 400d Galaxy Cluster Survey weak lensing programme: III: Evidence for consistent WL and X-ray masses at $z\approx 0.5$

Scaling properties of galaxy cluster observables with mass provide central insights into the processes shaping clusters. Calibrating proxies for cluster mass will be crucial to cluster cosmology with upcoming surveys like eROSITA and Euclid. The recent Planck results led to suggestions that X-ray masses might be biased low by $\sim\!40$ %, more than previously considered. We extend the direct calibration of the weak lensing -- X-ray mass scaling towards lower masses (as low as $1\!\times\!10^{14}\,\mathrm{M}_{\odot}$) in a sample representative of the $z\!\sim\!0.4$--$0.5$ population. We investigate the scaling of MMT/Megacam weak lensing (WL) masses for $8$ clusters at $0.39\!\leq\!z\!\leq\!0.80$ as part of the \emph{400d} WL programme with hydrostatic \textit{Chandra} X-ray masses as well as those based on the proxies, e.g. $Y_{\mathrm{X}}\!=\!T_{\mathrm{X}}M_{\mathrm{gas}}$. Overall, we find good agreement between WL and X-ray masses, with different mass bias estimators all consistent with zero. Subdividing the sample, we find the high-mass subsample to show no significant mass bias while for the low-mass subsample, there is a bias towards overestimated X-ray masses at the $\sim\!2σ$ level for some mass proxies. The overall scatter in the mass-mass scaling relations is surprisingly low. Neither observation can be traced back to the parameter settings in the WL analysis. We do not find evidence for a strong ($\sim\!40$ %) underestimate in the X-ray masses, as suggested to reconcile Planck cluster counts and cosmological constraints. For high-mass clusters, our measurements are consistent with studies in the literature. The mass dependent bias, significant at $\sim\!2σ$, may hint at a physically different cluster population (less relaxed clusters with more substructure and mergers); or it may be due to small number statistics.

astro-ph.CO↗

arXiv2014

Simple characters and coefficient systems on the building

Let F be a non-archimedean local field and G be the group GL(N,F). Let πbe a smooth complex representation of G lying in the Bernstein block B(π) of some simple type in the sense of Bushnell and Kutzko. Refining the approach of the second author and U. Stuhler, we canonically attach to πa subset X_πof the Bruhat-Tits building X of G, as well as a G-equivariant coefficient system C[π] on X_π. Roughly speaking the coefficient system is obtained by taking isotypic components of πaccording to some representations constructed from the Bushnell and Kutzko type of π. We conjecture that when πhas central character, the augmented chain complex associate to C[π] is a projective resolution of πin the category B(π). Moreover we reduce this conjecture to a technical lemma of representation theoretic nature. We prove this lemma when πis an irreducible discrete series of G. We then attach to any irreducible discrete series πof G an explicit pseudo-coefficient f_πand obtain a Lefschetz type formula for the value of the Harish-Chandra character of πat a regular elliptic element. In contrast to that obtained by U. Stuhler and the second author, this formula allows explicit character value computations.

math.RT↗