Limit theorems for the Matsumoto zeta-function

Limit theorems for the Matsumoto zeta-function

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Limit Representations of Riemann's Zeta Function

In this article, it is shown that Riemann’s zeta function ζ(s) admits two limit representations when <(s) > 1. Each of these limit representations is deduced by using simple arguments based upon the classical Tannery’s (limiting) theorem for series.

Limit Theorem with Weight for Lerch Zeta Function

Zeta function regularization in de Sitter space: the Minkowski limit

We study an integral representation for the zeta function of the one-loop effective potential for a minimally coupled massive scalar field in D-dimensional de Sitter spacetime. By deforming the contour of integration we present it in a form suitable for letting the de Sitter radius tend to infinity, and we demonstrate explicitly for the case D=2 that the quantities ζ(0) and ζ(0) have the approp...

Limit theorems for mergesort

Central and local limit theorems (including large deviations) are established for the number of comparisons used by the standard top-down recursive mergesort under the uniform permutation model. The method of proof utilizes Dirichlet series, Mellin transforms and standard analytic methods in probability theory.