Related papers: Partial zeta functions
We intimate deeper connections between the Riemann zeta and gamma functions than often reported and further derive a new formula for expressing the value of $\zeta(2n+1)$ in terms of zeta at other fractional points. This paper also…
By a similar idea for the construction of Milnor's gamma functions, we introduce "higher depth determinants" of the Laplacian on a compact Riemann surface of genus greater than one. We prove that, as a generalization of the determinant…
We study analytic properties of height zeta functions of equivariant compactifications of the Heisenberg group.
Building on the mapping relations between analytic functions and periodic functions using the abstract operators $\cos(h\partial_x)$ and $\sin(h\partial_x)$, and by defining the Zeta and related functions including the Hurwitz Zeta function…
We use partial zeta functions to analyse the asymptotic behaviour of certain smooth arithmetical sums over smooth k-free integers.
An analysis of the zeta and gamma function is presented, using elementary functions like [] and {}, a general formula for the angle of zeta(1/2 + i*n) is found and the same for the gamma function.
The aim of the present paper is to study the relations between the prime distribution and the zero distribution for generalized zeta functions which are expressed by Euler products and is analytically continued as meromorphic functions of…
The Hurwitz-type Euler zeta function is defined as a deformation of the Hurwitz zeta function: \begin{equation*} \zeta_E(s,x)=\sum_{n=0}^\infty\frac{(-1)^n}{(n+x)^s}. \end{equation*} In this paper, by using the method of Fourier expansions,…
It is the aim of these lectures to introduce some basic zeta functions and their uses in the areas of the Casimir effect and Bose-Einstein condensation. A brief introduction into these areas is given in the respective sections. We will…
This article extends classical one variable results about Euler products defined by integral valued polynomial or analytic functions to several variables. We show there exists a meromorphic continuation up to a presumed natural boundary,…
We introduce the multiple zeta functions with structures similar to those of symmetric functions such as Schur $P$-, Schur $Q$-, symplectic and orthogonal functions in the representation theory. We first consider their basic properties such…
We use the definition of a star (or Moyal or twisted) product to give a phasespace definition of the $\zeta$-function. This allows us to derive new closed expressions for the coefficients of the heat kernel in an asymptotic expansion for…
A new formula relating the analytic continuation of the Hurwitz zeta function to the Euler gamma function and a polylogarithmic function is presented. In particular, the values of the first derivative of the real part of the analytic…
A $q$-analogue of the Hurwitz zeta-function is introduced through considerations on the spectral zeta-function of quantum group $SU_{q}(2)$, and its analytic aspects are studied via the Euler-MacLaurin summation formula. Asymptotic formulas…
This work is dedicated to the promotion of the results Hadamard, Landau E., Walvis A., Estarmann T and Paul R. Chernoff for pseudo zeta functions. The properties of zeta functions are studied, these properties can lead to new regularities…
In this article, we study the multiple zeta functions (MZF) and some of its variants at identical arguments. Using the harmonic product, these functions can be expressed as polynomials in the Riemann zeta function. Firstly, we note that an…
We use a form of lifted harmonic analysis to develop a two-dimensional adelic integral representation of the zeta functions of simple arithmetic surfaces. Manipulations of this integral then lead to an adelic interpretation of the so-called…
A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structure, plus countably many special…
The main objective of this paper is to introduce a new extension of Hurwitz-Lerch Zeta function in terms of extended beta function. We then investigate its important properties such as integral representations, differential formulas, Mellin…
The paper reviews existing results about the statistical distribution of zeros for the three main types of zeta functions: number-theoretical, geometrical, and dynamical. It provides necessary background and some details about the proofs of…