Related papers: Functional equations for Weng's zeta functions for…

An invertible polynomial in $n$ variables is a quasihomogeneous polynomial consisting of $n$ monomials so that the weights of the variables and the quasi-degree are well defined. In the framework of the construction of mirror symmetric…

In the paper, we shall establish the existence of a meromorphic continuation of the Global Zeta Function $\zeta(f,\chi)$ of a Global Number Field $K$ and also deduce the functional equation for the same, using different properties of the…

Let $M$ be a finite volume, non-compact hyperbolic Riemann surface, possibly with elliptic fixed points, and let $\chi$ denote a finite dimensional unitary representation of the fundamental group of $M$. Let $\Delta$ denote the hyperbolic…

We formulate and prove the analogue of the Ramanujan Conjectures for modular forms of half-integral weight subject to some ramification restriction in the setting of a polynomial ring over a finite field. This is applied to give an…

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…

Let X be a regular scheme, projective and flat over Spec \mathbb Z. We give a conjectural formula, up to sign and powers of 2, for \zeta^*(X,r), the leading term in the series expansion of \zeta(X,s) at s=r, in terms of Weil-etale motivic…

We prove that the subgroup zeta function and the normal zeta function of a finitely generated virtually nilpotent group are finite sums of Euler products of cone integrals over $\mathbb{Q}$ and we deduce from this that they have rational…

For the Tornheim double zeta function T(s1,s2,s3) of complex variables,we obtain its functional equations,which are new.Using the calculus of r-th order derivative of zeta(s,alpha) as a function of alpha(developed in author[7])as the…

We examine "partition zeta functions" analogous to the Riemann zeta function but summed over subsets of integer partitions. We prove an explicit formula for a family of partition zeta functions already shown to have nice properties -- those…

We prove or conjecture several relations between the multizeta values for positive genus function fields of class number one, focusing on the zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or…

We generalize the Ihara-Selberg zeta function to hypergraphs in a natural way. Hashimoto's factorization results for biregular bipartite graphs apply, leading to exact factorizations. For $(d,r)$-regular hypergraphs, we show that a modified…

Explicit expressions for zonal spherical functions of $SO(p,q)$ matrix groups are obtained using a generalized hypergeometric series of two variables.

We define supersymmetric zeta functions and supersymmetric determinants, which can reveal spectral properties complementary to those captured by the supersymmetric indices. They play a crucial role in analyzing the Cardy-like behaviors of…

Let X be a complete, geometrically irreducible, singular, algebraic curve defined over a field of characteristic p big enough. Given a local ring O_{P,X} at a rational singular point P of X, we attached a universal zeta function which is a…

Let (G,V) be an irreducible prehomogeneous vector space defined over a number field k, P in k[V] a relative invariant polynomial, and X a rational character of G such that P(gx)=X(g)P(x). Let V_k^{ss}={x \in V_k such that P(x) is not equal…

We give a probabilistic interpretation of the Dedekind zeta functions of $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-2})$ using zeta integrals and use this to show that the first two Li coefficients of these zeta functions are positive.…

We produce explicit formulae for various ideal zeta functions associated to the members of an infinite family of class-$2$-nilpotent Lie rings, introduced in [1], in terms of Igusa functions. As corollaries we obtain information about…

We prove that the partial zeta function introduced in [9] is a rational function, generalizing Dwork's rationality theorem.

A unified algebraic interpretation of both finite families of orthogonal polynomials and biorthogonal rational functions of $q$-Hahn type is provided. The approach relies on the meta $q$-Hahn algebra and its finite-dimensional bidiagonal…

We give simple numerical bounds for $\zeta(s)$, $\vartheta(s)$, $\mathop{\mathcal R}(s)$, $Z(t)$, for use in the numerical computation of these functions. The purpose of the paper is to give bounds for several functions needed in the…