Related papers: Justification for zeta function regularization

A consistent procedure for regularization of divergences and for the subsequent renormalization of the string tension is proposed in the framework of the one-loop calculation of the interquark potential generated by the Polyakov-Kleinert…

A precise zeta-function calculation shows that the contribution of the vacuum energy to the observed value of the cosmological constant can possibly have the desired order of magnitude albeit the sign strongly depends on the topology of the…

A method to regularize and renormalize the fluctuations of a quantum field in a curved background in the $\zeta$-function approach is presented. The method produces finite quantities directly and finite scale-parametrized counterterms at…

We put forward the concept of measure graphs. These are (possibly uncountable) graphs equipped with an action of a groupoid and a measure invariant under this action. Examples include finite graphs, periodic graphs, graphings and…

The appearance of multiple zeta values in anomalous dimensions and $\beta$-functions of renormalizable quantum field theories has given evidence towards a motivic interpretation of these renormalization group functions. In this paper we…

Zeta function regularization is an effective method to extract physical significant quantities from infinite ones. It is regarded as mathematically simple and elegant but the isolation of the physical divergency is hidden in its analytic…

A scaling and renormalization approach to the Riemann zeta function, $\zeta$, evaluated at $-1$ is presented in two ways. In the first, one takes the difference between $U_{n}:=\sum_{q=1}^{n}q$ and $4U_{\left\lfloor \frac{n}{2}\right\rfloor…

The vacuum fluctuations give rise to a number of phenomena; however, the the Casimir Effect is arguably the most salient manifestation of the quantum vacuum. In its most basic form it is realized through the interaction of a pair of neutral…

We consider analytic functions of the Riemann zeta type, for which, if $s$ is a zero, so is $1-s$. We use infinite product representations of these functions, assuming their zeros to be of first order. We use exponential factors to…

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…

We propose a regularization technique and apply it to the Euler product of zeta functions, mainly of the Riemann zeta function, to make unknown some clear. In this paper that is the first part of the trilogy, we try to demonstrate the…

We consider the variation of two fundamental types of zeta functions that arise in the study of both physical and analytical problems in geometric settings involving conical singularities. These are the Barnes zeta functions and the Bessel…

The definitions and main properties of the Ihara and Bartholdi zeta functions for infinite graphs are reviewed. The general question of the validity of a functional equation is discussed, and various possible solutions are proposed.

We have proposed a regularization technique and apply it to the Euler product of zeta functions in the part one. In this paper that is the second part of the trilogy, we give another evidence to demonstrate the Riemann hypotheses by using…

There exists an infinite series of ratios by which one can derive the Riemann zeta function $\zeta(s)$ from Catalan numbers and central binomial coefficients which appear in the terms of the series. While admittedly the derivation is not…

We postulate the existence of a self-adjoint operator associated to a system with countably infinite number of degrees of freedom whose spectrum is the sequence of the nontrivial zeros of the Riemann zeta function. We assume that it…

For a divisor representing a function and another divisor representing a differential form on a normal surface singularity, there is a notion of motivic and topological zeta function. In this paper, given a finite morphism between two…

Zeta regularization has proven to be a powerful and reliable tool for the regularization of the vacuum energy density in ideal situations. With the Hadamard complement, it has been shown to provide finite (and meaningful) answers too in…

We study absolute zeta functions from the view point of a canonical normalization. We introduce the absolute Hurwitz zeta function for the normalization. In particular, we show that the theory of multiple gamma and sine functions gives good…

A Master equation has been previously obtained which allows the analytic integration of a fairly large family of functions provided that they possess simple properties. Here, the properties of this Master equation are explored, by extending…