Related papers: p-adic Gauss integrals from the Poison summarizing…

We overview results on the topic of Poisson approximation that are missed in existing surveys. The topic of Poisson approximation to the distribution of a sum of integer-valued random variables is presented as well. We do not restrict…

We derive special forms of the Poisson summation formula for even and odd functions, which are applied to obtain representations for Euler-type numbers and to sum various series related to elliptic functions.

In a paper in the American Mathematical Monthly, the corresponding author asks for an asymptotic of a gcd-sum function \begin{align}\sum_{ab\leq N}\tau(\gcd(a,b))\label{eqn:taugcdsum}\end{align} We extensively study generalizations of the…

This paper provides a technique for evaluating some nonlinear Gaussian sums in closed forms. The evaluation is obtained from the known values of simpler exponential sums.

Gaussian Quadrature is a well known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums have found some new interest. In this paper we apply these ideas to…

For two distinguished prime $\ell$ and $p$, we prove a $\ell$-adic version of the Poisson formula for reductive $p$-adic groups. In order to do this we write an identity for the trace of regular representation and orbital integrals. Next we…

We propose a simple method to reduce a general p-form electrodynamics with respect to the standard Gauss constraints. The canonical structure of the reduced theory displays a p-dependent sign which makes the essential difference between…

We prove a reciprocity formula between Gauss sums that is used in the computation of certain quantum invariants of 3-manifolds. Our proof uses the discriminant construction applied to the tensor product of lattices.

We present a novel approach to Gaussian Berezin correlation functions. A formula well known in the literature expresses these quantities in terms of submatrices of the inverse matrix appearing in the Gaussian action. By using a recently…

In this paper we study a group theoretical generalization of the well-known Gauss's formula that uses the generalized Euler's totient function introduced in [11].

In this short note, we give a very simple but useful generalization of a result of Vershynin (Theorem 5.39 of [1]) for a random matrix with independent sub-Gaussian rows. We also explain with an example where our generalization is useful.

We prove a Poisson summation formula for the zero locus of a quadratic form in an even number of variables with no assumption on the support of the functions involved. The key novelty in the formula is that all ``boundary terms'' are given…

We show that various identities from [1] and [3] involving Gould-Hopper polynomials can be deduced from the real but also complex orthogonal invariance of multivariate Gaussian distributions. We also deduce from this principle a useful…

In this paper, for the generalized Fibonacci sequence $\left\{W_n\left(a,b,p,q\right)\right\}$, by using elementary methods and techniques, we give the asymptotic estimation values of…

We compute the sum and the alternating sum of the reciprocals of triangular numbers using two standard methods from calculus: a telescoping series approach and a power series approach. We then extend these results to generalized…

We present an explicit evaluation of the double Gauss sum $\displaystyle G(a,b,c;S;p^n):=\sum_{x,y=0}^{p^n-1} e^{2\pi i S(ax^2+bxy+cy^2)/p^n}$, where $a, b, c$ are integers such that $\gcd(a,b,c)=1$, $p$ is a prime, $n$ is a positive…

We present an extremely simple solution to the renormalization of quantum electrodynamics based on Epstein-Glaser approach to renormalization theory.

Gaussian sum-rules relate a QCD prediction to a two-parameter Gaussian-weighted integral of a hadronic spectral function, providing a clear conceptual connection to quark-hadron duality. In contrast to Laplace sum-rules, the Gaussian…

We review our recent result on the rigorous derivation of the renormalized Gibbs measure from the many-body Gibbs state in 1D and 2D. The many-body renormalization is accomplished by simply tuning the chemical potential in the…

We give a parameterized generalization of the sum formula for quadruple zeta values. The generalization has four parameters, and is invariant under a cyclic group of order four. By substituting special values for the parameters, we also…