arXiv subjects

Yuetong Zhao

Publications and source records attributed to Yuetong Zhao.

18 recordsLinked to original sources

arXiv2026

Bounds for moments of twisted quadratic characters of prime modulus

We study, under the Generalized Riemann Hypothesis (GRH), the moments of sums of Fourier coefficients of a fixed holomorphic Hecke eigenform twisted by the quadratic character $\chi_{8p}$, where $p$ ranges over odd primes. We establish the correct order of magnitude for the unsmoothed $m$-th moment for all real $m\geq 4$, and a sharp upper bound of order $XY^{m/2}\,\, (\log X)^{m(m-3)/2}\,\,$ for the smoothed $m$-th moment for all integers $m\geq 4$. A matching lower bound for all even integers $m\geq 4$ shows that this bound is optimal.

math.NT↗

arXiv2026

Distance Estimation and Sky Localization of Eccentric Double White Dwarf Binaries from Gravitational Wave Observations inside Globular Clusters

The cosmic distance scale is built on multiple different techniques for estimating distances in space that are often connected and dependent on multiple measurements and assumptions. Double white dwarf binaries (DWDs) are common objects and are expected to produce gravitational wave (GW) signals that can be observed with space-based detectors such as LISA. By analyzing these signals we should be able to estimate the distance and sky location of the source. Previous studies have done this for circular binaries which, while they are abundant, have, in general, weaker signals than eccentric binaries and it is not possible to differentiate whether a circular binary is in the field or in a dense environment such as a globular cluster (GC). In this paper we used eccentric binaries from MOCCA GC simulations, simulated the GW signal from each binary at locations related to GCs in the Milky Way and estimated the precision on the distance and the sky location of the source. We find that distances can be estimated with higher precision than current day methods even with low eccentricity binaries and higher eccentricity further increases this precision. Although the probability of finding a tight and eccentric DWD is far lower than a circular one, we can expect to find at least a few in the dense environments of the Milky Way, such as GCs. These estimations would be independent measurements with high precision to objects inside dense environments, such as GCs inside the Milky Way and the Magellanic Clouds.

astro-ph.HE↗

arXiv2025

Multiband gravitational wave observations of eccentric escaping binary black holes from globular clusters

Stellar-mass binary black holes (sBBHs) formed in globular clusters (GCs) are promising sources for multiband gravitational wave (GW) observations, particularly with low- and middle-frequency detectors. These sBBHs can retain detectable eccentricities when they enter the sensitivity bands of low-frequency GW observatories. We study multiband GW observations of eccentric sBBHs that escape from GC models simulated with the MOCCA code, focusing on how low- and middle-frequency detectors can constrain their eccentricities and other parameters. Using Monte Carlo simulations, we generate ten realizations of cosmic sBBHs by combining the MOCCA sample with a cosmological model for GC formation and evolution. We then assess their detectability and the precision of parameter estimation. Our results show that LISA, Taiji, the LISA-Taiji network (LT), and AMIGO could detect $0.8\pm0.7$, $11.6\pm2.0$, $15.4\pm2.7$, and $7.9\pm1.3$ escaping sBBHs, respectively, over four years, while LT-AMIGO could detect $20.6\pm3.0$ multiband sBBHs in the same period. LT and AMIGO can measure initial eccentricities with relative errors of approximately $10^{-6}-2\times10^{-4}$ and $10^{-3}-0.7$, respectively. Joint LT-AMIGO observations have a similar ability to estimate eccentricities as LT alone.

astro-ph.HE↗

arXiv2025

Bounds for integral moments of quadratic twists of Fourier coefficients of modular forms

In this paper, we obtain under the assumption of the Generalized Riemann Hypothesis upper bounds for all high integral moments of sums of Fourier coefficients of a given modular form twisted by quadratic Dirichlet characters. We show the bounds are optimal by establishing unconditionally the corresponding lower bounds for all even integer moments.

math.NT↗

arXiv2025

Mean squares of quadratic twists of the Fourier coefficients of modular forms

In this paper, we evaluate asymptotically a smoothed version of the sum \[ \displaystyle \sideset{}{^*}\sum_{d \leq X} \left( \sum_{n \leq Y} \lambda_f(n)\Big(\frac{8d}{n}\Big)\right)^2, \] where $\Big ( \frac{8d}{\cdot}\Big )$ is the Kronecker symbol, $\sideset{}{^*}\sum$ denotes a sum over positive odd square-free integers and $\lambda_f(n)$ are Fourier coefficients of a given modular form $f$.

math.NT↗

arXiv2025

Formation Channels of Gravitationally Resolvable Double White Dwarf Binaries Inside Globular Clusters

Current gravitational wave detectors are sensitive to coalescing black holes and neutron stars. However, double white dwarfs (DWDs) have long been recognized as promising sources of gravitational waves, and upcoming detectors like LISA will be able to observe these systems in abundance. DWDs are expected to be the dominant gravitational wave (GW) sources in parts of the LISA frequency range, making it crucial to understand their formation for future detections. The Milky Way contains many white dwarfs (WDs) in both the field and star clusters, promising a rich population of DWDs for LISA. However, the large number of sources may make it difficult to resolve individual binaries, and DWDs in the field and clusters often have similar properties, complicating the identification of their origins from GW signals alone. In this work, we focus on eccentric and tight DWDs, which cannot form in the field, but require dynamical interactions in dense clusters to increase their eccentricity after circularization through mass transfer phases and common-envelope evolution during binary evolution. These binaries may also form in three- and four-body dynamical interactions where a DWD binary may directly form with high eccentricity and low separation. Our results show that we should expect eccentric and tight DWDs in clusters that can provide meaningful GW signal, however, the number is low; with an upper limit of 10-15 in the MW. These can be used to independently obtain distances of their host cluster.

astro-ph.SR↗

arXiv2024

Bounds for moments of quadratic Dirichlet character sums of prime moduli

Assuming the generalized Riemann hypothesis, we evaluate sharp upper bounds for the shifted moments of quadratic Dirichlet L-functions with moduli 8p, where p ranges over odd primes. We then apply this result to prove bounds for the moments of quadratic Dirichlet character sums with prime moduli.

math.NT↗

arXiv2024

On a multiplicative hybrid problem over almost-primes

Let N be a large enough natural number, A and B be subsets of {N+1, ... , 2N}. In this paper, we prove that there exists integers a, b with a belongs to A, b belongs to B such that ab=P_k^2 + O(P_k^{1-c}), where 0<c<1/2 and P_k denotes an almost-prime with at most k prime factors, counted with multiplicity.

math.NT↗

arXiv2024

An Empirical Study of Retrieval Augmented Generation with Chain-of-Thought

Since the launch of ChatGPT at the end of 2022, generative dialogue models represented by ChatGPT have quickly become essential tools in daily life. As user expectations increase, enhancing the capability of generative dialogue models to solve complex problems has become a focal point of current research. This paper delves into the effectiveness of the RAFT (Retrieval Augmented Fine-Tuning) method in improving the performance of Generative dialogue models. RAFT combines chain-of-thought with model supervised fine-tuning (SFT) and retrieval augmented generation (RAG), which significantly enhanced the model's information extraction and logical reasoning abilities. We evaluated the RAFT method across multiple datasets and analysed its performance in various reasoning tasks, including long-form QA and short-form QA tasks, tasks in both Chinese and English, and supportive and comparison reasoning tasks. Notably, it addresses the gaps in previous research regarding long-form QA tasks and Chinese datasets. Moreover, we also evaluate the benefit of the chain-of-thought (CoT) in the RAFT method. This work offers valuable insights for studies focused on enhancing the performance of generative dialogue models.

cs.CL↗

arXiv2023

Multiband gravitational wave observations of stellar binary black holes at the low to middle and high frequencies

The ground-based gravitational wave (GW) observatories discover a population of merging stellar binary black holes (BBHs), which are promising targets for multiband observations by the low-, middle-, and high-frequency GW detectors. In this paper, we investigate the multiband GW detections of BBHs and demonstrate the advantages of such observations in improving the localization and parameter estimates of the sources. We generate mock samples of BBHs by considering different formation models as well as the merger rate density constrained by the current observations (GWTC-3). We specifically consider the astrodynamical middle-frequency interferometer GW observatory (AMIGO) in the middle-frequency band and estimate that it may detect $21$-$91$ BBHs with signal-to-noise ratio $\varrho\geq8$ in a $4$-yr observation period. The multiband observations by the low-frequency detectors [Laser Interferometer Space Antenna (LISA) and Taiji] and AMIGO may detect $5$-$33$ BBHs with $\varrho_{\rm LT}\geq5$ and $\varrho_{\rm AMI}\geq5$, which can evolve to the high-frequency band within $4$ yr and can be detected by the Cosmic Explorer (CE) and Einstein Telescope (ET). The joint observations of LISA-Taiji-AMIGO-ET-CE may localize the majority of the detectable BBHs in sky areas of $7\times10^{-7}$ to $2\times10^{-3}$ deg$^2$, which is improved by a factor of $\sim120$, $\sim2.4\times10^{5}$, $\sim1.8\times10^{4}$, or $\sim1.2\times10^{4}$, comparing with those by only adopting CE-ET, AMIGO, LISA-Taiji, or LISA-Taiji-AMIGO. These joint observations can also lead to an improvement of the measurement precision of the chirp mass (symmetric mass ratio) by a factor of $\sim5.5\times10^{4}$ ($33$), $\sim16$ ($8$), $\sim120$ ($90$), or $\sim5$ ($5$), comparing with those by CE-ET, AMIGO, LISA-Taiji, or LISA-Taiji-AMIGO.

astro-ph.HE↗

arXiv2023

Sgap: Towards Efficient Sparse Tensor Algebra Compilation for GPU

Sparse compiler is a promising solution for sparse tensor algebra optimization. In compiler implementation, reduction in sparse-dense hybrid algebra plays a key role in performance. Though GPU provides various reduction semantics that can better utilize the parallel computing and memory bandwidth capacity, the central question is: how to elevate the flexible reduction semantics to sparse compilation theory that assumes serial execution. Specifically, we have to tackle two main challenges: (1) there are wasted parallelism by adopting static synchronization granularity (2) static reduction strategy limits optimization space exploration. We propose Sgap: segment group and atomic parallelism to solve these problems. Atomic parallelism captures the flexible reduction semantics to systematically analyze the optimization space of sparse-dense hybrid algebra on GPU. It is a new optimization technique beyond current compiler-based and open-source runtime libraries. Segment group elevates the flexible reduction semantics to suitable levels of abstraction in the sparse compilation theory. It adopts changeable group size and user-defined reduction strategy to solve challenge (1) and (2), respectively. Finally, we use GPU sparse matrix-matrix multiplication (SpMM) on the TACO compiler as a use case to demonstrate the effectiveness of segment group in reduction semantics elevation. We achieve up to 1.2x speedup over the original TACO's SpMM kernels. We also apply new optimization techniques found by atomic parallelism to an open-source state-of-the-art SpMM library dgSPARSE. We achieve 1.6x - 2.3x speedup on the algorithm tuned with atomic parallelism.

cs.DC↗

arXiv2022

Constraining the origin of stellar binary black hole mergers by detections of their lensed host galaxies and gravitational wave signals

A significant number of stellar binary black hole (sBBH) mergers may be lensed and detected by the third generation gravitational wave (GW) detectors. Their lensed host galaxies may be detectable, which thus helps to accurately localize these sources and provide a new approach to study the origin of sBBHs. In this paper, we investigate the detectability of the lensed host galaxies for the lensed sBBH mergers. We find that the detection fraction of the host galaxies to the lensed GW events can be significantly different for a survey with a given limiting magnitude if sBBHs are produced by different mechanisms, such as the evolution of massive binary stars, the dynamical interactions in dense star clusters, and that assisted by active galactic nuclei or massive black holes. Furthermore, we illustrate that the statistical spatial distribution of those lensed sBBHs in its hosts resulting from different sBBH formation channels can be different from each other. Therefore, with the third generation GW detectors and future large scale galaxy surveys, it is possible to independently constrain the sBBH origin via the detection fraction of those lensed events with identifiable lensing host signatures and/or even constrain the contribution fractions from different sBBH formation mechanisms

astro-ph.HE↗

arXiv2022

On Detecting Stellar Binary Black Holes via the LISA-Taiji Network

The detection of gravitational waves (GWs) by ground-based laser interferometer GW observatories (LIGO/Virgo) reveals a population of stellar binary black holes (sBBHs) with (total) masses up to $\sim 150M_\odot$, which are potential sources for space-based GW detectors, such as LISA and Taiji. In this paper, we investigate in details on the possibility of detecting sBBHs by the LISA-Taiji network in future. We adopt the sBBH merger rate density constrained by LIGO/VIRGO observations to randomly generate mock sBBHs samples. Assuming an observation period of $4$ years, we find that the LISA-Taiji network may detect several tens (or at least several) sBBHs with signal-to-noise ratio (SNR) $>8$ (or $>15$), a factor $2-3$ times larger than that by only using LISA or Taiji observations. Among these sBBHs, no more than a few that can merge during the $4$-year observation period. If extending the observation period to $10$ years, then the LISA-Taiji network may detect about one hundred (or twenty) sBBHs with SNR $>8$ (or $>15$), among them about twenty (or at least several) can merge within the observation period. Our results suggest that the LISA-Taiji network may be able to detect at least a handful to twenty or more sBBHs even if assuming a conservative SNR threshold ($15$) for ``detection'', which enables multi-band GW observations by space and ground-based GW detectors. We also further estimate the uncertainties in the parameter estimations of the sBBH systems ``detected'' by the LISA-Taiji network. We find that the relative errors in the luminosity distance measurements and sky localization are mostly in the range of $0.05-0.2$ and $1-100°^2$, respectively, for these sBBHs.

astro-ph.HE↗

arXiv2022

On Dark Gravitational Wave Standard Sirens as Cosmological Inference and Forecasting the Constraint on Hubble Constant using Binary Black Holes Detected by Deci-hertz Observatory

Gravitational wave (GW) signals from compact binary coalescences can be used as standard sirens to constrain cosmological parameters if their redshift can be measured independently. However, mergers of stellar binary black holes (BBHs) may not have electromagnetic counterparts and thus have no direct redshift measurements. These dark sirens may be still used to statistically constrain cosmological parameters by combining their GW measured luminosity distances and localization with deep redshift surveys of galaxies around it. We investigate this dark siren method in detail by using mock BBH and galaxy samples. We find that the Hubble constant can be constrained well with an accuracy $\lesssim1\%$ with a few tens or more of BBH mergers at redshift up to $1$ if GW observations can provide accurate estimates of their luminosity distance (with relative error of $\lesssim0.01$) and localization ($\lesssim0.1~\rm{deg}^2$), though the constraint may be significantly biased if the luminosity distance and localization errors are larger. We also introduce a simple method to correct this bias and find it is valid when the luminosity distance and localization errors are modestly large. We further generate mock BBH samples, according to current constraints on BBH merger rate and the distributions of BBH properties, and find that the Deci-hertz Observatory (DO) in a half year observation period may detect about one hundred BBHs with signal-to-noise ratio $\varrho\gtrsim30$, relative luminosity distance error $\lesssim0.02$, and localization error $\lesssim0.01\rm{deg}^2$. By applying the dark standard siren method, we find that the Hubble constant can be constrained to the $\sim0.1-1\%$ level using these DO BBHs, an accuracy comparable to the constraints obtained by using electromagnetic observations in the near future, thus it may provide insight into the Hubble tension.

astro-ph.CO↗

arXiv2020

Stochastic Gravitational Wave Background and Eccentric Stellar Compact Binaries

Gravitational wave (GW) radiations from numerous cosmic stellar-compact-binaries form a stochastic GW background (GWB), which is expected to be detected by ground and space GW detectors in future. Theoretical predictions of this GWB were mostly obtained by assuming either circular binaries and/or a specific channel for binary formation, which may have some uncertainties. In this paper, we estimate the GWB and its spectrum by using simple models for the formation of both stellar mass binary black holes (sBBHs) and binary neutron stars (BNSs). We consider that the dynamically originated sBBHs have relatively larger masses and higher eccentricities compared with those from field binary stars and its possible effect on the GWB spectrum. We find that the GWB spectrum may have a turnover in the low-frequency (Laser Interferometer Space Antenna; LISA) band and may be better described by a broken double power-law than a single power-law with the unique index $2/3$, and the low-frequency slope depends on the significance of the dynamically originated sBBHs with high eccentricities. We further generate mock samples of sBBHs and BNSs, and simulate the mock GWB strain in the time domain. We find that GWB can be detected with signal-to-noise ratio (SNR) $\gtrsim274/255/21$ by LISA/Taiji/TianQin over $5$-years' observation and $\gtrsim3$ by LIGO over $2$-years' observation. Furthermore, we estimate that the number of sBBHs that may be detected by LISA/Taiji/TianQin individually with SNR $\gtrsim8$ is $\sim5$-$221$/$7$-$365$/$3$-$223$ over $5$-years' observation.

astro-ph.HE↗

arXiv2020

On two Diophantine inequalities over primes (II)

Let $1<c<\frac{26088036}{12301745},c\not=2$ and $N$ be a sufficiently large real number. In this paper, it is proved that, for almost all $R\in (N,2N]$, the Diophantine inequality \begin{equation*} \big|p_1^c+p_2^c+p_3^c-R\big|<\log^{-1}N \end{equation*} is solvable in primes $p_1,p_2,p_3$. Moreover, we also prove that the following Diophantine inequality \begin{equation*} \big|p_1^c+p_2^c+p_3^c+p_4^c+p_5^c+p_6^c-N\big|<\log^{-1}N \end{equation*} is solvable in prime variables $p_1,p_2,p_3,p_4,p_5,p_6$, which improves the previous result $1<c<\frac{37}{18},c\neq2$.

math.NT↗

arXiv2018

Gravitational lensing of gravitational waves: A statistical perspective

In this paper, we study the strong gravitational lensing of gravitational waves (GWs) from a statistical perspective, with particular focus on the high frequency GWs from stellar binary black hole coalescences. These are most promising targets for ground-based detectors such as Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) and the proposed Einstein Telescope (ET) and can be safely treated under the geometrical optics limit for GW propagation. We perform a thorough calculation of the lensing rate, by taking account of effects caused by the ellipticity of lensing galaxies, lens environments, and magnification bias. We find that in certain GW source rate scenarios, we should be able to observe strongly lensed GW events once per year ($\sim1~\text{yr}^{-1}$) in the aLIGO survey at its design sensitivity; for the proposed ET survey, the rate could be as high as $\sim80~\text{yr}^{-1}$. These results depend on the estimate of GW source abundance, and hence can be correspondingly modified with an improvement in our understanding of the merger rate of stellar binary black holes. We also compute the fraction of four-image lens systems in each survey, predicting it to be $\sim30$ per cent for the aLIGO survey and $\sim6$ per cent for the ET survey. Finally, we evaluate the possibility of missing some images due to the finite survey duration, by presenting the probability distribution of lensing time delays. We predict that this selection bias will be insignificant in future GW surveys, as most of the lens systems ($\sim90$ per cent) will have time delays less than $\sim1$ month, which will be far shorter than survey durations.

astro-ph.CO↗

arXiv2017

Host galaxy properties of mergers of stellar binary black holes and their implications for advanced LIGO gravitational wave sources

Understanding the host galaxy properties of stellar binary black hole (SBBH) mergers is important for revealing the origin of the SBBH gravitational-wave sources detected by advanced LIGO and helpful for identifying their electromagnetic counterparts. Here we present a comprehensive analysis of the host galaxy properties of SBBHs by implementing semi-analytical recipes for SBBH formation and merger into cosmological galaxy formation model. If the time delay between SBBH formation and merger ranges from $\la$\,Gyr to the Hubble time, SBBH mergers at redshift $z\la0.3$ occur preferentially in big galaxies with stellar mass $M_*\ga2\times10^{10}\msun$ and metallicities $Z$ peaking at $\sim0.6Z_\odot$. However, the host galaxy stellar mass distribution of heavy SBBH mergers ($M_{\bullet\bullet}\ga50\msun$) is bimodal with one peak at $\sim10^9\msun$ and the other peak at $\sim2\times10^{10}\msun$. The contribution fraction from host galaxies with $Z\la0.2Z_\odot$ to heavy mergers is much larger than that to less heavy mergers. If SBBHs were formed in the early universe (e.g., $z>6$), their mergers detected at $z\la0.3$ occur preferentially in even more massive galaxies with $M_*>3\times10^{10}\msun$ and in galaxies with metallicities mostly $\ga0.2Z_\odot$ and peaking at $Z\sim0.6Z_\odot$, due to later cosmic assembly and enrichment of their host galaxies. SBBH mergers at $z\la0.3$ mainly occur in spiral galaxies, but the fraction of SBBH mergers occur in elliptical galaxies can be significant if those SBBHs were formed in the early universe; and about two thirds of those mergers occur in the central galaxies of dark matter halos. We also present results on the host galaxy properties of SBBH mergers at higher redshift.

astro-ph.GA↗