Related papers: Analytic Continuation of some zeta functions
Summation arithmetic functions with asymptotically independent terms are studied in the paper, the limit of which is the law of normal distribution. Assertions about the asymptotic behavior of the indicated functions are proved.
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.
The $L^2$-zeta function of an infinite graph Y (defined previously in a ball around zero) has an analytic extension. For a tower of finite graphs covered by Y, the normalized zeta functions of the finite graphs converge to the $L^2$-zeta…
This is an expository paper which gives a simple arithmetic introduction to the conjectures of Weil and Dwork concerning zeta functions of algebraic varieties over finite fields. A number of further open questions are raised.
Series of extended Epstein type provide examples of non-trivial zeta functions with important physical applications. The regular part of their analytic continuation is seen to be a convergent or an asymptotic series. Their singularity…
We introduce new non-abelian zeta functions for curves defined over finite fields. There are two types, i.e., pure non-abelian zetas defined using semi-stable bundles, and group zetas defined for pairs consisting of (reductive group,…
We study the theta function and the Hurwitz-type zeta function associated to the Lucas sequence $U=\{U_n(P,Q)\}_{n\geq 0}$ of the first kind determined by the real numbers $P,Q$ under certain natural assumptions on $P$ and $Q$. We deduce an…
The paper deals with lower bounds for the remainder term in asymptotics for a certain class of arithmetic functions. Typically, these are generated by a Dirichlet series which involves a product of Riemann zeta-functions of a special form.
We use partial zeta functions to analyse the asymptotic behaviour of certain smooth arithmetical sums over smooth k-free integers.
Holomorphic functions are amazing because their values in an ever so small disk in the complex plane completely determine the function values at arbitrary points in their maximum possible domain. The process of extending such a function…
In the present paper, firstly, we consider the Volterra integral equation of second type for a remainder term in an asymptotic formula of an arithmetic function which satisfies some special conditions and obtained a solution of the…
Using analytic torsion associated to stable bundles, we introduce zeta functions for compact Riemann surfaces. To justify the well-definedness, we analyze the degenerations of analytic torsions at the boundaries of the moduli spaces, the…
In this article, we introduce a notion of non-degeneracy, with respect to certain Newton polyhedra, for rational functions over non-Archimedean locals fields of arbitrary characteristic. We study the local zeta functions attached to…
Theta functions play a major role in many current researches and are powerful tools for studying integrable systems. The purpose of this paper is to provide a short and quick exposition of some aspects of meromorphic theta functions for…
We present another expression to regularize the Euler product representation of the Riemann zeta function. % in this paper. The expression itself is essentially same as the usual Euler product that is the infinite product, but we define a…
In this paper, for any positive integer $\ell\geq2,$ we define $\ell$-generalized Fibonacci zeta function. We then study its analytic continuation to the whole complex plane $\mathbb{C}.$ Further, we compute a possible list of singularities…
The global additive and multiplicative properties of Laplace type operators acting on irreducible rank 1 symmetric spaces are considered. The explicit form of the zeta function on product spaces and of the multiplicative anomaly is derived.
Following an idea of Nigel Higson, we develop a method for proving the existence of a meromor-phic continuation for some spectral zeta functions. The method is based on algebras of generalized differential operators. The main theorem…
In this paper we treat the classical Riemann zeta function as a function of three variables: one is the usual complex $\adyn$-dimensional, customly denoted as $s$, another two are complex infinite dimensional, we denote it as $\b =…
The paper considers asymptotics of summation functions of additive and multiplicative arithmetic functions. We also study asymptotics of summation functions of natural and prime arguments. Several assertions on this subject are proved and…