Estimates for Weyl sums in the theory of discrete universality

Athanasios Sourmelidis*

*Korrespondierende/r Autor/in für diese Arbeit

Publikation: Beitrag in einer FachzeitschriftArtikel

Abstract

We prove joint and disjoint discrete universality theorems for Dirichlet L-functions L(s,χ) and Hurwitz zeta-functions ζ(s;β) with rational parameter β∈(0,1]. Our approach does not utilize Gallagher’s lemma, which is usually employed to prove discrete universality theorems. In our case, however, this would lead to certain difficulties when it is about estimating discrete second moments of L-functions. Therefore, we introduce a novel approach which is based only on Euler product representations and zero-density estimates of L-functions, as well as mean-value estimates for Weyl sums.
Originalspracheenglisch
Seitenumfang23
FachzeitschriftThe Ramanujan Journal
Frühes Online-Datum8 Feb 2021
DOIs
PublikationsstatusElektronische Veröffentlichung vor Drucklegung. - 8 Feb 2021

ASJC Scopus subject areas

  • !!Algebra and Number Theory

Fingerprint

Untersuchen Sie die Forschungsthemen von „Estimates for Weyl sums in the theory of discrete universality“. Zusammen bilden sie einen einzigartigen Fingerprint.

Dieses zitieren