Related papers: Zeta functions of orders on surfaces
We present highlights of computations of the Riemann zeta function around large values and high zeros. The main new ingredient in these computations is an implementation of the second author's fast algorithm for numerically evaluating…
In this paper we study the higher-order Euler numbers and polynomials and we introduce the mutiple zeta functions which interpolate higher-order Euler polynomials and numbers at negative integers
In this paper we study spectral zeta functions associated to finite and infinite graphs. First we establish a meromorphic continuation of these functions under some general conditions. Then we study special values in the case of standard…
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…
The (partially) ordered set of the non-trivial zeros of the zeta function with positive imaginary parts is considered. The order is the coordinatewise order inherited from $\mathbb{C}$. Some interesting properties regarding the minimal…
We establish upper bounds for moments of zeta sums using results on shifted moments of the Riemann zeta function under the Riemann hypothesis.
We consider multi-polylogarithm functions which are slightly different from the ordinary ones. These functions have two integral representations and an order structure similar to those of multiple zeta star values. We also give a necessary…
Ramanujan investigated maximal order for the number of divisors function by introducing some notion such as (superior) highly composite numbers. He also studied maximal order for other arithmetic functions including the sum of powers of…
We determine what isogeny classes of supersingular abelian surfaces over a finite field k of characteristic 2 contain jacobians. We deal with this problem in a direct way by computing explicitly the zeta function of all supersingular curves…
In this paper we define a symmetric zeta function. We show that it can be analytically continued to a meromorphic function on $\mathbb{C}^3$ with only simple poles at some special hyperplanes. We also calculate the value of a multiple…
In this paper, we study the computation of optimal discrete Morse functions on stratifolds. In particular, we present an algorithm that efficiently computes such functions for a broad class of them. Moreover, we characterize the conditions…
The aim of this paper is to describe explicitly the poles of the meromorphic continuation of the Igusa local zeta function associated to several polynomials. Using resolution of singularities is possible to express the Igusa's local zeta…
In this article, we investigate high moments of zeta sums $\sum_{n\le x}n^{i t}$. We show unconditional lower bounds for them.
We implement a noncommutative analogue of the well-known commutative cyclic covering trick and implement it to explicitly construct a vast collection of numerically Calabi-Yau orders, noncommutative analogues of surfaces of Kodaira…
We prove by an elementary method the Riemann hypothesis for the local Euler factor of the zeta function of quadratic orders.
In this paper we study the twisted Shintani zeta function over number fields.
This paper investigates a new family of special functions referred to as hypergeometric zeta functions. Derived from the integral representation of the classical Riemann zeta function, hypergeometric zeta functions exhibit many properties…
We give an explicit formula for the motivic zeta function in terms of a log smooth model. It generalizes the classical formulas for snc-models, but it gives rise to much fewer candidate poles, in general. As an illustration, we explain how…
We use partial zeta functions to analyse the asymptotic behaviour of certain smooth arithmetical sums over smooth k-free integers.
In this paper, it is demonstrated that derived equivalence between smooth, projective, connected schemes that are either surfaces or abelian implies equality of zeta functions.