Related papers: Zeta-Dimension
We study relationships between spinor representations of certain Lie algebras and Lie superalgebras of differential operators on the circle and values of $\zeta$--functions at the negative integers. By using formal calculus techniques we…
The algebra of big zeta values we introduce in this paper is an intermediate object between multiple zeta values and periods of the multiple zeta motive. It consists of number series generalizing multiple zeta values, the simplest examples,…
Let $A$ be a set of finite integers, define $$A+A \ = \ \{a_1+a_2: a_1,a_2 \in A\}, \ \ \ A-A \ = \ \{a_1-a_2: a_1,a_2 \in A\},$$ and for non-negative integers $s$ and $d$ define $$sA-dA\ =\ \underbrace{A+\cdots+A}_{s}…
Fractional superstrings are recently-proposed generalizations of the traditional superstrings and heterotic strings. They have critical spacetime dimensions which are less than ten, and in this paper we investigate model-building for the…
This paper is a continuation of our work on theta and zeta functions In the previous papers we considered the case of even dimensional rank one symmetric spaces of non-compact type. The present is concerned with the odd-dimensional case,…
In this paper, some new results are reported for the study of Riemann zeta function $\zeta(s)$ in the critical strip $0<Re(s)<1$, such as $\zeta(s)$ expressed in a generalized Euler product only involving prime numbers. Particularly, some…
In this paper, we study various twisted A-harmonic sums, named following the seminal log-algebraicity papers of G. Anderson. These objects are partial sums of new types of special zeta values introduced by the first author and linked to…
The Argand diagram is used to display some characteristics of the Riemann Zeta function. The zeros of the Zeta function on the complex plane give rise to an infinite sequence of closed loops, all passing through the origin of the diagram.…
We represent the Riemann zeta function in the half-plane $\Re s >1$ via series whose terms admit geometrically decreasing bounds. Due to an underlying recurrence relation, which is used to compute coefficients entering into the terms, the…
First, let the fractal dimension D=n(integer)+d(decimal), so the fractal dimensional matrix was represented by a usual matrix adds a special decimal row (column). We researched that mathematics, for example, the fractal dimensional linear…
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…
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 theory of Ihara zeta functions is extended to non-compact arithmetic quotients of Bruhat-Tits trees. This new zeta function turns out to be a rational function, despite the infinite-dimensional setting. In general it has zeros and…
The harmonic sawtooth map w(x) of the unit interval onto itself is defined where it is shown that its fixed points are enumerated by generating functions involving the golden ratio in their parameters. The appropriately scaled Mellin…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
By using ideas and strong results borrowed from the classical moment problem, we show how -under very general conditions- a discrete number of values of the spectral zeta function (associated generically with a non-decreasing sequence of…
The volume of the unit sphere in every dimension is given a new interpretation as a product of special values of the zeta function of $\mathbb{Z}$, akin to volume formulas of Minkowski and Siegel in the theory of arithmetic groups. A…
Many examples of zeta functions in number theory and combinatorics are special cases of a construction in homotopy theory known as a decomposition space. This article aims to introduce number theorists to the relevant concepts in homotopy…
In this report we present experimental results using \emph{Haussdorf-Besicovich} fractal dimension for performing morphological galaxy classification. The fractal dimension is a topological, structural and spatial property that give us…
Using a summation identity obtained for the Fourier coefficients of $x^{2k}$, we derive a closed form expression for the zeta function at even positive integers, using a technique similar to one in an existing proof by Aladdi and Defant[1],…