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

We prove that the special value conjecture for the Zeta function of a proper, regular arithmetic scheme X that we formulated in our previous article [8] is compatible with the functional equation of the Zeta function provided that the…

We prove and conjecture several relations between multizeta values for $\mathbb{F}_q[t]$, focusing on zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or equivalently algebraic). In particular,…

In this article we introduce a new type of local zeta functions and study some connections with pseudodifferential operators in the framework of non-Archimedean fields. The new local zeta functions are defined by integrating complex powers…

For a general Fuchsian group of the first kind with an arbitrary unitary representation we define zeta functions related to the contributions of the identity, hyperbolic, elliptic and parabolic conjugacy classes in Selberg's trace formula.…

We consider the prehomogeneous vector space of pairs of ternary quadratic forms. For the lattice of pairs of integral ternary quadratic forms and its dual lattice, there are six zeta functions associated with the the prehomogeneous vector…

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…

For a germ of a meromorphic function f=P/Q, we offer notions of the monodromy operators at zero and at infinity. If the holomorphic functions P and Q are non-degenerated with respect to their Newton diagrams, we give an analogue of the…

We show that the motivic zeta functions of smooth, geometrically connected curves with no rational points are rational functions. This was previously known only for curves whose smooth projective models have a rational point on each…

This paper generalizes Bass' work on zeta functions for uniform tree lattices. Using the theory of von Neumann algebras, machinery is developed to define the zeta function of a discrete group of automorphisms of a bounded degree tree. The…

We derive explicit formulae for the subalgebra zeta functions of all higher Heisenberg Lie algebras over an arbitrary compact discrete valuation ring $\mathfrak{o}$. To this end, we develop Hecke-theoretic techniques for the enumeration, by…

We show that the notion of zeta functions over F1, as given in special cases by Soule', extends naturally to all F1-schemes as defined earlier by the author. We further give two constructions of K-theory for affine schemes or F1-rings, we…

We provide a framework for relating certain q-series defined by sums over partitions to multiple zeta values. In particular, we introduce a space of polynomial functions on partitions for which the associated q-series are q-analogues of…

In the present paper we give a simple mathematical foundation for describing the zeros of the Selberg zeta functions $Z_X$ for certain very symmetric infinite area surfaces $X$. For definiteness, we consider the case of three funneled…

In the former part of this paper, we give functional equations for Barnes multiple zeta-functions and consider some relevant results. In particular, we show that Ramanujan's classical formula for the Riemann zeta values can be derived from…

We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.

We compute the representation zeta functions of some finitely generated nilpotent groups associated to unipotent group schemes over rings of integers in number fields. These group schemes are defined by Lie lattices whose presentations are…

We define the generalized Dirichlet beta and Riemann zeta functions in terms of the integrals, involving powers of the hyperbolic secant and cosecant functions. The corresponding functional equations are established. Some consequences of…

A simple and elementary derivation of values at integer points for the Riemann's zeta and related functions is reported.

Some zeta functions which are naturally attached to the locally homogeneous vector bundles over compact locally symmetric spaces of rank one are investigated. We prove that such functions can be expressed in terms of entire functions whose…

We prove that for a compact locally symmetric Riemannian space $M$ of rank 1 there exist infinitely many automorphic Tate motives $f$ such that the generalized Selberg zeta function $Z_{M(f)}(s)$ satisfies a simple functional equation in…