Related papers: The quaternionic weighted zeta function of a graph
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…
We study some infinite products of absolute zeta functions. Especially, we consider the convergence and the rationality of them.
We show that the zeta function of a regular graph admits a representation as a quotient of a determinant over a $L^2$-determinant of the combinatorial Laplacian.
We provide a coherent overview of a number of recent results obtained by the authors in the theory of schemes defined over the field with one element. Essentially, this theory encompasses the study of a functor which maps certain geometries…
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…
The reciprocal of the Ihara zeta function of a graph is a polynomial invariant introduced by Ihara in 1966. Scott and Storm gave a method to determine the coefficients of the polynomial. Here we simplify their calculation and determine the…
The Dedekind zeta function of a quadratic number field factors as a product of the Riemann zeta function and the $L$-function of a quadratic Dirichlet character. We categorify this formula using objective linear algebra in the abstract…
We introduce a new type of multiple zeta functions, which we call bilateral zeta functions, analogous to the Barnes zeta functions. The bilateral zeta function is a periodic function and shares certain basic properties of Barnes zeta…
In the present paper we introduce some expansions, based on the falling factorials, for the Euler Gamma function and the Riemann Zeta function. In the proofs we use the Fa\'a di Bruno formula, Bell polynomials, potential polynomials,…
Let X be a regular scheme, projective and flat over the integers. Let A be the constant in the conjectured functional equation for the zeta-function of X. We give a conjecture computing A in terms of Euler characteristics of derived…
We investigate spectral quantities of quantum graphs by expanding them as sums over pseudo orbits, sets of periodic orbits. Only a finite collection of pseudo orbits which are irreducible and where the total number of bonds is less than or…
A new, seemingly useful presentation of zeta functions on complex tori is derived by using contour integration. It is shown to agree with the one obtained by using the Chowla-Selberg series formula, for which an alternative proof is thereby…
This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite…
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 topological zeta function of a matroid is a rational function as well as a valuative invariant of the matroid, encoding rich combinatorial information. We analyze topological zeta functions of matroids from the vantage point of several…
We study the distribution of large (and small) values of several families of $L$-functions on a line $\text{Re(s)}=\sigma$ where $1/2<\sigma<1$. We consider the Riemann zeta function $\zeta(s)$ in the $t$-aspect, Dirichlet $L$-functions in…
It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system which is called fractal interpolation function. We generalize the notion of fractal…
In this paper, we give a short elementary proof of the well known Euler's recurrence formula for the Riemann zeta function at positive even integers and integral representations of the Riemann zeta function at positive integers and at…
We prove a connection between Schmidt-rank and weight of quadratic forms. This provides a new tool for the classification of graph states based on entanglement. Our main tool arises from a reformulation of previously known results…
This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…