Related papers: Zeta functions of infinite graph bundles

We present a method for computing the zeta function of a smooth projective variety over a finite field which proceeds by induction on the dimension. We have implemented our approach for some surfaces using the Magma programming language,…

In this paper, we introduce (local and) global non-abelian zeta functions for general curves. As an example, we compute the so-called rank two zeta functions for genus two curves by studying non-abelian Brill-Noether loci and their…

We calculate zeta functions for certain orders of rank $3$ defined by standard integral table algebras and integral fusion rings that have irrational-valued irreducible characters. The calculations are obtained from explicit calculations of…

Curves over finite fields are of great importance in cryptography and coding theory. Through studying their zeta-functions, we would be able to find out vital arithmetic and geometric information about them and their Jacobians, including…

Let $\mathbf{G}$ be a unipotent group scheme defined in terms of a nilpotent Lie lattice over the ring $\mathcal{O}$ of integers of a number field. We consider bivariate zeta functions of groups of the form $\mathbf{G}(\mathcal{O})$…

The reciprocal of the Ihara zeta function of a graph is a polynomial invariant introduced by Ihara in 1966. Scott and Storm gave a method to determine the coefficients of the polynomial. Here we simplify their calculation and determine the…

Spectral functions, such as the zeta functions, are widely used in Quantum Field Theory to calculate physical quantities. In this work, we compute the electrostatic potential and field due to an infinite discrete distribution of point…

We associate motivic zeta functions to a large class of infinite dimensional Lie algebras

The zeta function of a curve $C$ over a finite field may be expressed in terms of the characteristic polynomial of a unitary matrix $\Theta_C$. We develop and present a new technique to compute the expected value of…

We propose a novel fermionic model on the graphs. The Dirac operator of the model consists of deformed incidence matrices on the graph and the partition function is given by the inverse of the graph zeta function. We find that the…

We prove a general convergence result for zeta functions of prehomogeneous vector spaces extending results of H. Saito, F. Sato and Yukie. Our analysis points to certain subspaces which yield boundary terms. We study it further in the setup…

We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…

In the present paper, we prove an identity for the generating function of the quadruple zeta values. Taking homogeneous parts on both sides of the identity and substituting appropriate values for the variables, we obtain the sum formula for…

Using the fact that a finite sum of power series are given by the difference between two zeta functions, we justify the usage of the zeta function with a negative variable in physical problems to avoid the divergence of the infinite sum. We…

The sum formula is a well known relation in the field of the multiple zeta values. In this paper, we present its generalization for the Euler-Zagier multiple zeta function.

We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.

We develop techniques for computing zeta functions associated with nilpotent groups, not necessarily associative algebras, and modules, as well as Igusa-type zeta functions. At the heart of our method lies an explicit convex-geometric…

We give an explicit representation for the sums of multiple zeta-star values of fixed weight and height in terms of Riemann zeta values.

For each $(m+1)$-tuple ${\bf n}_m=(n_0,n_1,\ldots,n_m)$ of positive integers, the ${\bf n}_m$-derived zeta function $\widehat\zeta_{X,\mathbb F_q}^{\,({\bf n}_m)}(s)$ is defined for a curve $X$ over $\mathbb F_q$. This derived zeta function…

We provide a lower bound for the dimension of the vector space spanned by 1 and by the values of the Riemann Zeta function at the first odd integers. As a consequence, the Zeta function takes infinitely many irrational values at odd…