Value distribution of some non-classical zeta-functions

Author:

Algirdas JAVTOKAS

AMS Classification:

11M41

Keywords:

bicomplex numbers, bicomplex zeta-function, Hurwitz zeta-function, non-classical zeta-functions, periodic zeta-function, universality

Abstract:

This paper is a survey of author's thesis [7], where the value-distribution of some non-classical zeta-functions is considered. The main attention is devoted to the universality property of the periodic Hurwitz zeta-function \zeta(s,\alpha;\mathfrak{a}). Also, a bicomplex Hurwitz zeta-function is defined for the first time and convergence of its series and analytical continuation are investigated. Moreover, in the thesis we provide a link between the Euclidean action and the geometric zeta-function. Also, a distribution of poles of the geometric zeta-function is investigated.

Download paper:

javtokas-08.pdf

Vol. 3 (11), 2008