相关论文: Spectral Reciprocity: A Fourier--Analytic Approach
An approach to visualize the accessible reciprocal space accounting the goniometer angles limitation and the resolution element in the reciprocal space is presented. The shapes of the accessible reciprocal space region for coplanar and…
We derive an exact expression for the correlation function in redshift shells including all the relativistic contributions. This expression, which does not rely on the distant-observer or flat-sky approximation, is valid at all scales and…
A general algorithm for calculating the reflection and refraction of nonuniform plane waves from an arbitrarily oriented and charged planar interface between two lossy isotropic media is proposed based on the decomposition of the complex…
In the spirit of the Head-Gordon-Pople algorithm, we report vertical, transfer and horizontal recurrence relations for the efficient and accurate computation of four-electron integrals over Gaussian basis functions. Our recursive approach…
We show entireness of complete adjoint L-functions associated to \textbf{any} cuspidal representations of $\GL(3)$ or $\GL(4)$ over an arbitrary global field. Twisted cases are also investigated.
This paper presents a novel factorization-based, low-rank regularization method for solving multidimensional deconvolution problems in the frequency domain. In this approach, each frequency component of the unknown wavefield is represented…
Motivated by ongoing measurements at JILA, we calculate the recoil-free spectra of dipolar interacting fermions, for example ultracold heteronuclear molecules, in a one-dimensional lattice of two-dimensional pancakes, spectroscopically…
We study a variety of problems in the spectral theory of automorphic forms using entirely analytic techniques such as Selberg trace formula, asymptotics of Whittaker functions and behavior of heat kernels. Error terms for Weyl's law and an…
We perform an all-sky analysis of the general relativistic galaxy power spectrum using the well-developed spherical Fourier decomposition. Spherical Fourier analysis expresses the observed galaxy fluctuation in terms of the spherical…
We develop a field theory for spin glasses using Replica Fourier Transforms (RFT). We present the formalism for the case of replica symmetry and the case of replica symmetry breaking on an ultrametric tree, with the number of replicas $n$…
Following a strategy suggested by Michel--Venkatesh, we study the cubic moment of automorphic $L$-functions on $\operatorname{PGL}_2$ using regularized diagonal periods of products of Eisenstein series. Our main innovation is to produce…
In this paper a spectral-Lagrangian method for the Boltzmann equation for a multi-energy level gas is proposed. Internal energy levels are treated as separate species and inelastic collisions (leading to internal energy excitation and…
We introduce a fast Fourier spectral method for the spatially homogeneous Boltzmann equation with non-cutoff collision kernels. Such kernels contain non-integrable singularity in the deviation angle which arise in a wide range of…
We have introduced a new method for computing gravitational-wave emission from nonspinning binaries which systematically unifies the various integrals arising in the Fourier expansions of post-Newtonian dynamics, providing a simple,…
Reciprocal transformations mix the role of the dependent and independent variables to achieve simpler versions or even linearized versions of nonlinear PDEs. These transformations help in the identification of a plethora of PDEs available…
The identification of sampling sets that enable unique signal recovery is fundamental to many applications in signal processing and remains a central problem in mathematical analysis. Recent studies in the mathematical literature,…
The framework of relativistic self-consistent mean-field models is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to…
Planar N=4 SYM theory and QCD share the gluon sector, suggesting the investigation of Gribov-Lipatov reciprocity in the supersymmetric theory. Since the AdS/CFT correspondence links N=4 SYM and superstring dynamics on AdS5xS5, reciprocity…
The $SL(3)$ Kuznetsov formula exists in several versions, and has been employed with some success to study automorphic forms on $SL(3)$. In each version, the weight functions on the geometric side are given by multiple integrals with…
We establish several formulas relating periods of modular forms on quaternion algebras over number fields to special values of L-functions. Our main inputs are the cohomological techniques for working with periods introduced in [Mol21],…