A random variable related to the Hurwitz zeta-function with algebraic parameter

TL;DR

This paper introduces a new random variable linked to the Hurwitz zeta-function with algebraic parameters, establishing a limit theorem and showing approximation of complex numbers by its values.

Contribution

It presents a novel random variable related to the Hurwitz zeta-function and proves a limit theorem involving its distribution, with applications to approximation of complex numbers.

Findings

Limit measure described by the law of the new random variable

Any complex number can be approximated by Hurwitz zeta-function values with algebraic irrational parameters

Finite exceptions in the approximation results

Abstract

In this paper, we introduce a certain random variable closely related to the value-distribution of the Hurwitz zeta-function with algebraic parameter. We prove a version of the limit theorem, where the limit measure is presented by the law of this random variable. Then we apply it to show that any complex number can be approximated by values of the Hurwitz zeta-function for algebraic irrational parameters but with finite exceptions.