Related papers: Functional equations for local normal zeta functio…

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 consider families of Calabi-Yau n-folds containing singular fibres and study relations between the occurring singularity structure and the decomposition of the local Weil zeta-function. For 1-parameter families, this provides new…

It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the hole complex plane. In this paper, certain cases of specific (non-real analytic) smooth functions…

Formulas for the topological zeta functions of suspensions by 2 points are due to Artal et al. We generalize these formulas to the motivic level and for arbitrary suspensions, by using a stratification principle and classical techniques of…

This paper is dedicated to the description of the poles of the Igusa local zeta functions $Z(s,f,v)$ when $f(x,y)$ satisfies a new non degeneracy condition, that we have called arithmetic non degeneracy. More precisely, we attach to each…

In this paper, we give an explicit formula of the Shintani double zeta functions with any ramification in the most general setting of adeles over an arbitrary number field. Three applications of the explicit formula are given. First, we…

Let $f$ be a polynomial function over the complex numbers and let $\phi$ be a smooth function over $\mathbb{C}$ with compact support. When $f$ is non-degenerate with respect to its Newton polyhedron, we give an explicit list of candidate…

We introduce new methods from p-adic integration into the study of representation zeta functions associated to compact p-adic analytic groups and arithmetic groups. They allow us to establish that the representation zeta functions of…

Suppose $G$ is a $\mathcal{T}$-group (finitely generated torsion-free nilpotent) with centralizers outside of the derived subgroup being abelian of rank equal to $\text{rank}(Z_1)+1$. This includes the class of free nilpotent groups…

We define generalised zeta functions associated to indefinite quadratic forms of signature (g-1,1) -- and more generally, to complex symmetric matrices whose imaginary part has signature (g-1,1) -- and we investigate their properties. These…

We prove Patterson's conjecture about the singularities of the Selberg zeta function associated to a convex-cocompact, torsion free group acting on a hyperbolic space.

The zeta-function of a manifold is closely related to, and sometimes can be calculated completely, in terms of its periods. We report here on a practical and computationally rapid implementation of this procedure for families of Calabi-Yau…

This paper investigates a new family of special functions referred to as hypergeometric zeta functions. Derived from the integral representation of the classical Riemann zeta function, hypergeometric zeta functions exhibit many properties…

This article introduces and investigates the basic features of a dynamical zeta function for group actions, motivated by the classical dynamical zeta function of a single transformation. A product formula for the dynamical zeta function is…

In this paper, we prove the rationality of Igusa's local zeta functions of semiquasihomogeneous polynomials with coefficients in a non-archimedean local field K. The proof of this result is based on Igusa's stationary phase formula and some…

We initiate the study of spectral zeta functions $\zeta_{X}$ for finite and infinite graphs $X$, instead of the Ihara zeta function, with a perspective towards zeta functions from number theory and connections to hypergeometric functions.…

We compute the zeta functions enumerating graded ideals in the graded Lie rings associated with the free $d$-generator Lie rings $\mathfrak{f}_{c,d}$ of nilpotency class $c$ for all $c\leq2$ and for $(c,d)\in\{(3,3),(3,2),(4,2)\}$. We apply…

We consider pro-isomorphic zeta functions of the groups $\Gamma(\mathcal{O}_K)$, where $\Gamma$ is a unipotent group scheme defined over $\mathbb{Z}$ and $K$ varies over all number fields. Under certain conditions, we show that these…

In this paper, we introduce and study two new types of non-abelian zeta functions for curves over finite fields, which are defined by using (moduli spaces of) semi-stable vector bundles and non-stable bundles. A Riemann-Weil type hypothesis…

The Mordell-Tornheim zeta function and the Herglotz-Zagier function $F(x)$ are two important functions in Mathematics. By generalizing a special case of the former, namely $\Theta(z, x)$, we show that the theories of these functions are…