arXiv subjects

Chris Williams

Publications and source records attributed to Chris Williams.

28 records · Page 2Linked to original sources

arXiv2017

P-adic L-functions for GL(2)

Since Rob Pollack and Glenn Stevens used overconvergent modular symbols to construct p-adic L-functions for non-critical slope rational modular forms, the theory has been extended to construct p-adic L-functions for non-critical slope automorphic forms over totally real and imaginary quadratic fields by the first and second authors respectively. In this paper, we give an analogous construction over a general number field. In particular, we start by proving a control theorem stating that the specialisation map from overconvergent to classical modular symbols is an isomorphism on the small slope subspace. We then show that if one takes the modular symbol attached to a small slope cuspidal eigenform, then there is a canonical way of constructing a ray class distribution from the corresponding overconvergent symbol, that moreover interpolates critical values of the L-function of the eigenform. We thus define its p-adic L-function to be this distribution.

math.NT↗

arXiv2017

$\mathcal{L}$-invariants and exceptional zeros of Bianchi modular forms

Let f be a Bianchi modular form, that is, an automorphic form for GL(2) over an imaginary quadratic field F. In this paper, we prove an exceptional zero conjecture in the case where f is new at a prime above p. More precisely, for each prime $\mathfrak{p}$ of F above p we prove the existence of an L-invariant $\mathcal{L}_{\mathfrak{p}}$, depending only on $\mathfrak{p}$ and f, such that when the p-adic L-function of f has an exceptional zero at $\mathfrak{p}$, its derivative can be related to the classical L-value multiplied by $\mathcal{L}_{\mathfrak{p}}$. The proof uses cohomological methods of Darmon and Orton, who proved similar results for GL(2) over the rationals. When p is not split and f is the base-change of a classical modular form F, we relate $\mathcal{L}_{\mathfrak{p}}$ to the L-invariant of F, resolving a conjecture of Trifković in this case.

math.NT↗

arXiv2017

Lifting non-ordinary cohomology classes for SL(3)

In this paper, we present a generalisation of a theorem of David and Rob Pollack. In 'A construction of rigid analytic cohomology classes for congruence subgroups of SL(3,Z)', they give a very general argument for lifting ordinary eigenclasses (with respect to a suitable operator) in the group cohomology of certain arithmetic groups. With slightly tighter conditions, we prove the same result for non-ordinary classes. Pollack and Pollack apply their results to the case of p-ordinary classes in the group cohomology of congruence subgroups for SL3, constructing explicit overconvergent classes in this setting. As an application of our results, we give an extension of their results to the case of non-critical slope classes in the same setting.

math.NT↗

arXiv2015

$P$-adic $L$-functions of Bianchi modular forms

The theory of overconvergent modular symbols, developed by Rob Pollack and Glenn Stevens, gives a beautiful and effective construction of the $p$-adic $L$-function of a modular form. In this paper, we give an analogue of their results for Bianchi modular forms, that is, modular forms over imaginary quadratic fields. In particular, we prove control theorems that say that the canonical specialisation map from overconvergent to classical Bianchi modular symbols is an isomorphism on small slope eigenspaces of suitable Hecke operators. We also give an explicit link between the classical modular symbol attached to a Bianchi modular form and critical values of its $L$-function, which then allows us to construct $p$-adic $L$-functions of Bianchi modular forms.

math.NT↗

arXiv2014

Serendipitous discovery of a dying Giant Radio Galaxy associated with NGC 1534, using the Murchison Widefield Array

Recent observations with the Murchison Widefield Array at 185~MHz have serendipitously unveiled a heretofore unknown giant and relatively nearby ($z = 0.0178$) radio galaxy associated with NGC\,1534. The diffuse emission presented here is the first indication that NGC\,1534 is one of a rare class of objects (along with NGC\,5128 and NGC\,612) in which a galaxy with a prominent dust lane hosts radio emission on scales of $\sim$700\,kpc. We present details of the radio emission along with a detailed comparison with other radio galaxies with disks. NGC1534 is the lowest surface brightness radio galaxy known with an estimated scaled 1.4-GHz surface brightness of just 0.2\,mJy\,arcmin$^{-2}$. The radio lobes have one of the steepest spectral indices yet observed: $α=-2.1\pm0.1$, and the core to lobe luminosity ratio is $<0.1$\%. We estimate the space density of this low brightness (dying) phase of radio galaxy evolution as $7\times10^{-7}$\,Mpc$^{-3}$ and argue that normal AGN cannot spend more than 6\% of their lifetime in this phase if they all go through the same cycle.

astro-ph.GA↗

arXiv2014

The Murchison Widefield Array Commissioning Survey: A Low-Frequency Catalogue of 14,110 Compact Radio Sources over 6,100 Square Degrees

We present the results of an approximately 6,100 square degree 104--196MHz radio sky survey performed with the Murchison Widefield Array during instrument commissioning between 2012 September and 2012 December: the Murchison Widefield Array Commissioning Survey (MWACS). The data were taken as meridian drift scans with two different 32-antenna sub-arrays that were available during the commissioning period. The survey covers approximately 20.5 h < Right Ascension (RA) < 8.5 h, -58 deg < Declination (Dec) < -14 deg over three frequency bands centred on 119, 150 and 180 MHz, with image resolutions of 6--3 arcmin. The catalogue has 3-arcmin angular resolution and a typical noise level of 40 mJy/beam, with reduced sensitivity near the field boundaries and bright sources. We describe the data reduction strategy, based upon mosaiced snapshots, flux density calibration and source-finding method. We present a catalogue of flux density and spectral index measurements for 14,110 sources, extracted from the mosaic, 1,247 of which are sub-components of complexes of sources.

astro-ph.IM↗

arXiv2012

Observations of transients and pulsars with LOFAR international stations and the ARTEMIS backend

The LOw Frequency ARray - LOFAR - is a new radio interferometer designed with emphasis on flexible digital hardware instead of mechanical solutions. The array elements, so-called stations, are located in the Netherlands and in neighbouring countries. The design of LOFAR allows independent use of its international stations, which, coupled with a dedicated backend, makes them very powerful telescopes in their own right. This backend is called the Advanced Radio Transient Event Monitor and Identification System (ARTEMIS). It is a combined software/hardware solution for both targeted observations and real-time searches for millisecond radio transients which uses Graphical Processing Unit (GPU) technology to remove interstellar dispersion and detect millisecond radio bursts from astronomical sources in real-time.

astro-ph.IM↗

arXiv2012

Fast Holographic Deconvolution: a new technique for precision radio interferometry

We introduce the Fast Holographic Deconvolution method for analyzing interferometric radio data. Our new method is an extension of A-projection/software-holography/forward modeling analysis techniques and shares their precision deconvolution and widefield polarimetry, while being significantly faster than current implementations that use full direction-dependent antenna gains. Using data from the MWA 32 antenna prototype, we demonstrate the effectiveness and precision of our new algorithm. Fast Holographic Deconvolution may be particularly important for upcoming 21 cm cosmology observations of the Epoch of Reionization and Dark Energy where foreground subtraction is intimately related to the precision of the data reduction.

astro-ph.IM↗

arXiv2012

Observations of transients and pulsars with LOFAR international stations

The LOw FRequency ARray - LOFAR is a new radio telescope that is moving the science of radio pulsars and transients into a new phase. Its design places emphasis on digital hardware and flexible software instead of mechanical solutions. LOFAR observes at radio frequencies between 10 and 240 MHz where radio pulsars and many transients are expected to be brightest. Radio frequency signals emitted from these objects allow us to study the intrinsic pulsar emission and phenomena such as propagation effects through the interstellar medium. The design of LOFAR allows independent use of its stations to conduct observations of known bright objects, or wide field monitoring of transient events. One such combined software/hardware solution is called the Advanced Radio Transient Event Monitor and Identification System (ARTEMIS). It is a backend for both targeted observations and real-time searches for millisecond radio transients which uses Graphical Processing Unit (GPU) technology to remove interstellar dispersion and detect millisecond radio bursts from astronomical sources in real-time using a single LOFAR station.

astro-ph.IM↗

arXiv2003

Staging Transformations for Multimodal Web Interaction Management

Multimodal interfaces are becoming increasingly ubiquitous with the advent of mobile devices, accessibility considerations, and novel software technologies that combine diverse interaction media. In addition to improving access and delivery capabilities, such interfaces enable flexible and personalized dialogs with websites, much like a conversation between humans. In this paper, we present a software framework for multimodal web interaction management that supports mixed-initiative dialogs between users and websites. A mixed-initiative dialog is one where the user and the website take turns changing the flow of interaction. The framework supports the functional specification and realization of such dialogs using staging transformations -- a theory for representing and reasoning about dialogs based on partial input. It supports multiple interaction interfaces, and offers sessioning, caching, and co-ordination functions through the use of an interaction manager. Two case studies are presented to illustrate the promise of this approach.

cs.IR↗