Related papers: Monodromy Zeta Function Formula for Embedded $\mat…

We consider a composite generalized quantum integrable model solvable by the nested algebraic Bethe ansatz. Using explicit formulas of the action of the monodromy matrix elements onto Bethe vectors in the GL(3)-based quantum integrable…

Let $F$ be a finite field of order $q$ and characteristic $p$. Let $\mathbb{Z}_F=F[t]$, $\mathbb{Q}_F=F(t)$, $\mathbb{R}_F=F((1/t))$ equipped with the discrete valuation for which $1/t$ is a uniformizer, and let…

We generalize the construction of elliptic stable envelopes to actions of connected reductive groups and give a direct inductive proof of their existence and uniqueness in a rather general situation. We show these have powerful enumerative…

The enumeration of points on (or off) the union of some linear or affine subspaces over a finite field is dealt with in combinatorics via the characteristic polynomial and in algebraic geometry via the zeta function. We discuss the basic…

We introduce the etale framework to study Igusa zeta functions in several variables, generalizing the machinery of vanishing cycles in the univariate case. We define the etale Alexander modules, associated to a morphism of varieties F from…

We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.

The two-dimensional inhomogeneous zeta-function series (with homogeneous part of the most general Epstein type): \[ \sum_{m,n \in \mbox{\bf Z}} (am^2+bmn+cn^2+q)^{-s}, \] is analytically continued in the variable $s$ by using zeta-function…

In this paper we define and study a Dedekind-like zeta function for the algebra of multicomplex numbers. By using the idempotent representations for such numbers, we are able to identify this zeta function with the one associated to a…

We write down the functional equation of the zeta function of a global field. This equation is implicit in Weil's ``Basic Number Theory''.

The sum formula for finite and symmetric multiple zeta values, established by Wakabayashi and the authors, implies that if the weight and depth are fixed and the specified component is required to be more than one, then the values sum up to…

For each field k, we define an abelian category of rationally decomposed mixed motives with integer coefficients. When k is finite, we show that the category is Tannakian, and we prove formulas relating the behaviour of zeta functions near…

We assign an arbitrary density matrix to a weighted graph and associate to it a graph zeta function that is both a generalization of the Ihara zeta function and a special case of the edge zeta function. We show that a recently developed…

Let $\Gamma$ be a finite group acting linearly on $\C^n$, freely outside the origin, and let $N$ be the number of conjugacy classes of $\Gamma$ minus one. A construction of Kronheimer of moduli spaces $X_\zeta$ of translation-invariant…

Enumerating integral orbits in prehomogeneous vector spaces plays an important role in arithmetic statistics. We describe a method of proving subconvexity of the zeta function enumerating the integral orbits, illustrated by proving a…

We present some completely monotonic functions involving the$q$-polygamma functions, our result generalizes some known results.

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…

Multiple q-zeta values are a 1-parameter generalization (in fact, a q-analog) of the multiple harmonic sums commonly referred to as multiple zeta values. These latter are obtained from the multiple q-zeta values in the limit as q tends to…

Formulas for the most general case of the zeta function associated to a quadratic+linear+constant form (in {\bf Z}) are given. As examples, the spectral zeta functions $\zeta_\alpha (s)$ corresponding to bosonic ($\alpha =2$) and to…

There exists an infinite series of ratios by which one can derive the Riemann zeta function $\zeta(s)$ from Catalan numbers and central binomial coefficients which appear in the terms of the series. While admittedly the derivation is not…

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…