Related papers: Archimedean zeta integrals on U(n,1)

In the first part of this series of papers we propose a functional integral representation for local Archimedean L-factors given by products of the Gamma-functions. In particular we derive a representation of the Gamma-function as a…

In this paper, we study the Selberg and Ruelle zeta functions on compact hyperbolic odd dimensional manifolds. These zeta functions are defined on one complex variable $s$ in some right half-plane of $\mathbb{C}$. We use the Selberg trace…

We develop a practical method for computing local zeta functions of groups, algebras, and modules in fortunate cases. Using our method, we obtain a complete classification of generic local representation zeta functions associated with…

This note is a short survey of two topics: Archimedean zeta functions and Archimedean oscillatory integrals. We have tried to portray some of the history of the subject and some of its connections with similar devices in mathematics. We…

In various contexts, the zeta function of an object splits into a product of $L$-functions. We categorify this product formula for quadratic covers of objects in the following contexts: quadratic extensions of number fields, ramified double…

The aim of this paper is to describe explicitly the poles of the meromorphic continuation of the Igusa local zeta function associated to several polynomials. Using resolution of singularities is possible to express the Igusa's local zeta…

We consider two integrals over $x\in [0,1]$ involving products of the function $\zeta_1(a,x)\equiv \zeta(a,x)-x^{-a}$, where $\zeta(a,x)$ is the Hurwitz zeta function, given by $$\int_0^1\zeta_1(a,x)\zeta_1(b,x)\,dx\quad\mbox{and}\quad…

For the Tornheim double zeta function T(s1,s2,s3) of complex variables,we obtain its functional equations,which are new.Using the calculus of r-th order derivative of zeta(s,alpha) as a function of alpha(developed in author[7])as the…

Let $n \geq 1$ be an odd integer. We construct an anticyclotomic Euler system for certain cuspidal automorphic representations of unitary groups with signature $(1, 2n-1)$.

For a general Fuchsian group of the first kind with an arbitrary unitary representation we define zeta functions related to the contributions of the identity, hyperbolic, elliptic and parabolic conjugacy classes in Selberg's trace formula.…

This paper exposes the underlying mechanism for obtaining second integral moments of $GL_2$ automorphic $L$--functions over an arbitrary number field. Here, moments for $GL_2$ are presented in a form enabling application of the structure of…

For cofinite Kleinian groups, with finite-dimensional unitary representations, we derive the Selberg trace formula. As an application we define the corresponding Selberg zeta-function and compute its divisor, thus generalizing results of…

It is known that the Selberg zeta function for the modular group has an expression in terms of the class numbers and the fundamental units of the indefinite binary quadratic forms. In the present paper, we generalize such a expression to…

This article is a companion to several works of the author and others on the arithmetic of automorphic forms for GSp(4), and their associated L-functions and Galois representations. These works require, at various points, an input from…

In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…

As automorphic $L$-functions or Artin $L$-functions, several classes of $L$-functions have Euler products and functional equations. In this paper we study the zeros of $L$-functions which have the Euler products and functional equations. We…

We show that the finite part of the adjoint $L$ function (including contributions from all nonarchimedean places, including ramified places) is holomorphic in $\Re(s) \ge 1/2$ for a cuspidal automorphic representation of $GL_3$ over a…

For cofinite Kleinian groups (or equivalently, finite-volume three-dimensional hyperbolic orbifolds) with finite-dimensional unitary representations, we evaluate the regularized determinant of the Laplacian using W. Muller's regularization.…

In this article, we compute the Gan-Gross-Prasad period integral of Klingen Eisenstein series over the unitary group $\mathrm{U}(m+1, n+1)$ with a cuspidal automorphic form over $\mathrm{U}(m+1, n)$, and show that it is related to certain…

By using the method of iterated integral representations of series, we establish some explicit relationships between multiple zeta values and Integrals of logarithmic functions. As applications of these relations, we show that multiple zeta…