Related papers: Archimedean Zeta Functions and Oscillatory Integra…
This paper is divided into two independent parts. The first part presents new integral and series representations of the Riemaan zeta function. An equivalent formulation of the Riemann hypothesis is given and few results on this formulation…
This note contains a short proof of the functional equation for the zeta function.
In this paper we give some interesting identities between Euler numbers and zeta functions. Finally we will give the new values of Euler zeta function at positive even integers.
We define the generalized Dirichlet beta and Riemann zeta functions in terms of the integrals, involving powers of the hyperbolic secant and cosecant functions. The corresponding functional equations are established. Some consequences of…
In this note we explore the relationship between the operation of convolution of functions and the Eulerian integrals. This approach allow us to obtain some expressions for the convolution of a certain class of functions in terms of the…
The purpose of this note is to give a brief overview on zeta functions of curve singularities and to provide some evidences on how these and global zeta functions associated to singular algebraic curves over perfect fields relate to each…
Aspects of the properties, enumeration and construction of points on diagonal and Hermitian surfaces have been considered extensively in the literature and are further considered here. The zeta function of diagonal surfaces is given as a…
The Argand diagram is used to display some characteristics of the Riemann Zeta function. The zeros of the Zeta function on the complex plane give rise to an infinite sequence of closed loops, all passing through the origin of the diagram.…
In this essay I will give a strictly subjective selection of different types of zeta functions. Instead of providing a complete list, I will rather try to give the central concepts and ideas underlying the theory. This article is going to…
Partial zeta functions of algebraic varieties over finite fields generalize the classical zeta function by allowing each variable to be defined over a possibly different extension field of a fixed finite field. Due to this extra variation…
Contour integral representations for Riemann's Zeta function and Dirichelet's Eta (alternating Zeta) function are presented and investigated. These representations flow naturally from methods developed in the 1800's, but somehow they do not…
Along the recently trodden path of studying certain number theoretic properties of gauge theories, especially supersymmetric theories whose vacuum manifolds are non-trivial, we investigate Ihara's Graph Zeta Function for large classes of…
In this paper, we partially extend recent results of Wan concerning the relationship between the zeta functions of a Calabi-Yau hypersurface and its (singular) mirror variety.
This paper deals with some simple results about spherical functions of type $\delta$, namely new integral formulas, new results about behavior at infinity and some facts about the related $C_\sigma$ functions.
The definitions and main properties of the Ihara and Bartholdi zeta functions for infinite graphs are reviewed. The general question of the validity of a functional equation is discussed, and various possible solutions are proposed.
A technique for evaluating the electromagnetic Casimir energy in situations involving spherical or circular boundaries is presented. Zeta function regularization is unambiguously used from the start and the properties of Bessel and related…
Let F be a local non-archimedean field. We prove a formula relating orbital integrals in GL(n,F) (for the unit Hecke function) and the generating series counting ideals of a certain ring. Using this formula, we give an explicit estimate for…
Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…
This paper discusses the simplest examples of spectral zeta functions, especially those associated with graphs, a subject which has not been much studied. The analogy and the similar structure of these functions, such as their parallel…
We prove an equivalent of the Riemann hypothesis in terms of the functional equation (in its asymmetrical form) and the $a$-points of the zeta-function, i.e., the roots of the equation $\zeta(s)=a$, where $a$ is an arbitrary fixed complex…