Related papers: Partial zeta functions, partial exponential sums, …

In this paper we study spectral zeta functions associated to finite and infinite graphs. First we establish a meromorphic continuation of these functions under some general conditions. Then we study special values in the case of standard…

We introduce certain lattice sums associated with hyperplane arrangements, which are (multiple) sums running over integers, and can be regarded as generalizations of certain linear combinations of zeta-functions of root systems. We also…

This paper establishes new bridges between number theory and modern harmonic analysis, namely between the class of complex functions, which contains zeta functions of arithmetic schemes and closed with respect to product and quotient, and…

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…

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 prove that the zeta-function $\zeta_\Delta$ of the Laplacian $\Delta$ on a self-similar fractals with spectral decimation admits a meromorphic continuation to the whole complex plane. We characterise the poles, compute their residues,…

One of the generalizations of multiple zeta values is the $q$-version, and in the case of finite sums, they may be expressed explicitly in polynomial form. Several results have been found when the powers of the factors in the denominator…

This paper deals with the study of the behaviour of the value semigroup of a curve singularity define over a global field reduced modulo a maximal ideal. We also define a global zeta function of the curve by means of motivic integration…

We consider the variation of two fundamental types of zeta functions that arise in the study of both physical and analytical problems in geometric settings involving conical singularities. These are the Barnes zeta functions and the Bessel…

We define a zeta function of a finite graph derived from time evolution matrix of quantum walk, and give its determinant expression. Furthermore, we generalize the above result to a periodic graph.

The spectral zeta functions have been found many application in several branches of modern physics, including the quantum field theory, the string theory and the cosmology. In this paper, we shall consider the spectral zeta functions and…

In this paper,we develop a novel representation of the zeta function expressed as the limiting difference between two structured double sums. This approach leads to a new and elegant identity involving maximum functions and additive terms,…

In this brief note, we consider p-adic unit roots or poles of L-functions of exponential sums defined over finite fields. In particular, we look at the number of unit roots or poles, and a congruence relation on the units. This raises a…

A generalization of the Apery-like numbers, which is used to describe the special values $\zeta_Q(2)$ and $\zeta_Q(3)$ of the spectral zeta function for the non-commutative harmonic oscillator, are introduced and studied. In fact, we give a…

Standard zeta function regularisation enforces a scale-independent prescription for spectral aggregation, effectively fixing the relative weight of spectral contributions. We relax this constraint by replacing the derivative at $s=0$ with a…

We define zeta functions for the adjoint action of GL(n) on its Lie algebra and study their analytic properties. For n<4 we are able to fully analyse these functions, and recover the Shintani zeta function for the prehomogeneous vector…

In 2005, Kayal suggested that Schoof's algorithm for counting points on elliptic curves over finite fields might yield an approach to factor polynomials over finite fields in deterministic polynomial time. We present an exposition of his…

We consider a family of isometric extensions of the full shift on p symbols (for p a prime) parametrized by a probability space. Using Heath-Brown's work on the Artin conjecture, it is shown that for all but two primes p the set of limit…

On the critical line the conditional distribution of the zeta function's magnitude around zeta zeros exists and predicts the well-known pair correlation between nontrivial zeta zeros. However, this conditional distribution does not exist at…

Let $p$ and $l$ be rational primes such that $l$ is odd and the order of $p$ modulo $l$ is even. For such primes $p$ and $l$, and for $e=l, 2l$, we consider the non-singular projective curves $aY^e = bX^e + cZ^e$ ($abc \neq 0$) defined over…