相关论文: Partial zeta functions

Analyzing in detail the analytic continuation of the Riemann zeta function we are able to generate several new identities which may be useful for application in physics and mathematics.

In this paper, we generalize the partial fraction decomposition which is fundamental in the theory of multiple zeta values, and prove a relation between Tornheim's double zeta functions of three complex variables. As applications, we give…

We examine "partition zeta functions" analogous to the Riemann zeta function but summed over subsets of integer partitions. We prove an explicit formula for a family of partition zeta functions already shown to have nice properties -- those…

By restricting the variables running over various (possibly different) subfields, we introduce the notion of a partial zeta function. We prove that the partial zeta function is rational in an interesting case, generalizing Dwork's well…

We prove that a certain conjecture holds true and the conjecture states a relationship between the zeta function of a finite category and the Euler characteristic of a finite category.

In this paper we introduce new generalizations of the zeta function, the Tricomi functions; their main properties are studied. This opens the way to a deeper, better application of these functions both in the theory of special functions,…

A simple and elementary derivation of values at integer points for the Riemann's zeta and related functions is reported.

The manuscript reviews Dirichlet Series of important multiplicative arithmetic functions. The aim is to represent these as products and ratios of Riemann zeta-functions, or, if that concise format is not found, to provide the leading…

We study analytic properties of the pair consisting of a rather general form of zeta-function with an Euler product and a periodic Hurwitz zeta-function with a transcendental parameter. We first survey briefly previous results, and then…

We study analytic properties of the representation zeta functions of arithmetic groups of type $\mathsf{A}_2$, such as $\textrm{SL}_3(\mathbb{Z})$. In particular, we uncover further poles of these functions and determine a natural boundary…

We study the behaviour near s=1/2 of zeta functions of varieties over finite fields F_q with q a square. The main result is an Euler-characteristic formula for the square of the special value at s=1/2. The Euler-characteristic is…

In this paper we develop the analytic theory of a multiple zeta function in d independent complex variables defined over a global function field. This is the function field analog of the Euler-Zagier multiple zeta function of depth d.

In this paper, we investigate the shuffle product relations for Euler-Zagier multiple zeta functions as functional relations. To this end, we generalize the classical partial fraction decomposition formula and give two proofs. One is based…

We propose a regularization technique and apply it to the Euler product of zeta functions, mainly of the Riemann zeta function, to make unknown some clear. In this paper that is the first part of the trilogy, we try to demonstrate the…

We investigate analytic properties of height zeta functions of toric bundles over flag varieties.

Using elementary methods we find surprising connections between the values of the Riemann Zeta Function over integers and the fractional parts of rational powers, and a connection between the Riemann Zeta Function and the Prime Zeta…

In this manuscript, we give effective methods for computing the zeta function of maximal orders on surfaces.

This note contains a short proof of the functional equation for the zeta function.

We obtain formulas for the coefficients of positive and negative powers of a partial theta function.

In the present paper, we treat multidimensional polynomial Euler products with complex coefficients on ${\mathbb{R}}^d$. We give necessary and sufficient conditions for the multidimensional polynomial Euler products to generate infinitely…