Suppose Y is a regular covering of a graph X with covering transformation group π = Z. This paper gives an explicit formula for the L2 zeta function of Y and computes examples. When π = Z, the L2 zeta function is an algebraic function. As a consequence it extends to a meromorphic function on a Riemann surface. The meromorphic extension provides a setting to generalize known properties of zeta f...

Firstly, we prove a functional relation for the Tornheim double zeta function. Using this functional relation, we obtain simple proofs of some known formulas for special values of Tornheim and Euler-Zagier double zeta functions. Secondly, we obtain functional relations for Witten zeta functions by using a double L-values relation. By these functional relations, we obtain new proofs of known res...

The use of elliptic and hyperelliptic curves in cryptography relies on the ability to compute the Jacobian order of a given curve. Recently, Satoh proposed a probabilistic polynomial time algorithm to test whether the Jacobian – over a finite field Fq – of a hyperelliptic curve of the form Y 2 = X + aX + bX (with a, b ∈ Fq) has a large prime factor. His approach is to obtain candidates for the ...

Mathematisch-naturwissenschaftlichen Fakultät Doctor of Philosophy Twisted Second Moments and Explicit Formulae of the Riemann Zeta-Function by Nicolas Martinez Robles Verschiedene Aspekte, die analytische Zahlentheorie und die Riemann zeta-Funktion verbinden, werden erweitert. Dies beinhaltet: 1. explizite Formeln, die eine Verbindung zwischen der Möbiusfunktion und den nichttrivialen Nullstel...

LITP 4 place Jussieu 75005 Paris Abs t rac t Motivated by symbolic dynamics and algebraic geometry over finite fields, we define cyclic languages and the zeta function of a language. The main result is that the zeta function of a cyclic language which is recognizable by a finite automaton is rational. I. In t roduct ion Motivated by algebraic geometry over finite fields and symbolic dynamics, w...

In this chapter, we will see a proof of the analytic continuation of the Riemann zeta function ζ(s) and the Dirichlet L function L(s, χ) via the Hurwitz zeta function. This then gives rise to a functional equation for ζ(s) and a direct computation for the value of this function at negative integer points. 1. The Hurwitz zeta function We have already seen the definition of the Riemann zeta funct...

A weak version of the Ihara formula is proved for zeta functions attached to quotients of the Bruhat-Tits building of PGL3. This formula expresses the zeta function in terms of Hecke-Operators. It is the first step towards an arithmetical interpretation of the combinatorially defined zeta function.

The zeta family includes zeta, eta, and FcepsilonRIgamma (Fcgamma). Dimers of the zeta family proteins function as signal transducing subunits of the T cell antigen receptor (TCR), the pre-TCR, and a subset of Fc receptors. In mice lacking zeta/eta chains, T cell development is impaired, yet low numbers of CD4+ and CD8+ T cells develop. This finding suggests either that pre-TCR and TCR complexe...

We introduce and study elliptic zeta values, a two-parameter deformation of the values of Riemann’s zeta function at positive integers. They are essentially Taylor coefficients of the logarithm of the elliptic gamma function, and share the SL(3,Z) modular properties of this function. Elliptic zeta values at even integers are related to Eisenstein series and thus to sums of odd powers of divisor...

This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators {Tm : m ≥ 1} given by Tm(f )(a, c) = 1 m ∑m−1 k=0 f ( a+k m ,mc) acting on certain spaces of real-analytic functions, including Lerch zeta functions for various parameter values. The actions of various related operators on these function spaces are de...