Universality of the Hurwitz zeta-function on the half plane of absolute convergence
Number Theory
2020-08-12 v1 Complex Variables
Abstract
Let be a compact set with connected complement on the half-plane Re, and let be a continuous function on which is analytic in its interior. We prove that for any parameter then may be uniformly approximated arbitrarily closely by on for some , where denote the Hurwitz zeta-function. This is the first known universality result that is also known to hold for the Hurwitz zeta-function with an algebraic irrational parameter.
Keywords
Cite
@article{arxiv.2008.04709,
title = {Universality of the Hurwitz zeta-function on the half plane of absolute convergence},
author = {Johan Andersson},
journal= {arXiv preprint arXiv:2008.04709},
year = {2020}
}
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16 pages