Related papers: Building lattices and zeta functions

We study multiple zeta values and their generalizations from the point of view of Rota--Baxter algebras. We obtain a general framework for this purpose and derive relations on multiple zeta values from relations in Rota--Baxter algebras.

Using analytic torsion associated to stable bundles, we introduce zeta functions for compact Riemann surfaces. To justify the well-definedness, we analyze the degenerations of analytic torsions at the boundaries of the moduli spaces, the…

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,…

Lattice field theories with a complex action can be studied numerically by allowing a complexified configuration space to be explored. Here we compare the recently introduced formulation on a Lefschetz thimble with the result from…

The author introduced models of linear logic known as ''Interaction Graphs'' which generalise Girard's various geometry of interaction constructions. In this work, we establish how these models essentially rely on a deep connection between…

We introduce the multiple zeta functions with structures similar to those of symmetric functions such as Schur $P$-, Schur $Q$-, symplectic and orthogonal functions in the representation theory. We first consider their basic properties such…

The definition and main properties of the Ihara zeta function for graphs are reviewed, focusing mainly on the case of periodic simple graphs. Moreover, we give a new proof of the associated determinant formula, based on the treatment…

Relying on the Hurwitz formula, we find sums of the series over sine and cosine functions through the Hurwitz zeta function. Using another summation formula for these trigonometric series, we find finite sums of some series over the Riemann…

Serre in "Trees" laid down the fundamentals of the theory of groups acting on simplicial trees. In particular, Bass-Serre theory makes it possible to extract information about the structure of a group from its action on a simplicial tree.…

In this paper, we expand the theory of Weierstrassian elliptic functions by introducing auxiliary zeta functions $\zeta_\lambda$, zeta differences of first kind $\Delta_\lambda$ and second kind $\Delta_{\lambda,\mu}$ where…

In these notes, we explore possible stable properties for the zeta function of a geometric Zp-tower of curves over a finite field of characteristic p, in the spirit of Iwasawa theory. A number of fundamental questions and conjectures are…

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

We determine the special values at positive integers of the spectral zeta function associated with the combinatorial Laplacian on the regular tree. These values admit explicit formulas in terms of certain polynomials, which we show to be…

Partial zeta functions of algebraic varieties over finite fields generalize the classical zeta function by allowing each variable to be defined over a possibly different extension field of a fixed finite field. Due to this extra variation…

The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…

We review generalized zeta functions built over the Riemann zeros (in short: "superzeta" functions). They are symmetric functions of the zeros that display a wealth of explicit properties, fully matching the much more elementary Hurwitz…

Analytic-bilinear approach for construction and study of integrable hierarchies is discussed. Generalized multicomponent KP and 2D Toda lattice hierarchies are considered. This approach allows to represent generalized hierarchies of…

Let $L$ be a solvable Lie algebra of dimension less than or equal to 4 over finite fields. We compute and record, in explicit symbolic form, the zeta functions enumerating subalgebras or ideals of $L$, and study their properties. We also…

It is a well-known result that the proportion of lattice points visible from the origin is given by $\frac{1}{\zeta(2)}$, where $\zeta(s)=\sum_{n=1}^\infty\frac{1}{n^s}$ denotes the Riemann zeta function. Goins, Harris, Kubik and Mbirika,…

A generalized Toda Lattice equation is considered. The associated linear problem (Lax representation) is found. For simple case N=3 the $\tau$-function Hirota form is presented that allows to construct an exast solutions of the equations of…