Estimates for Weyl sums in the theory of discrete universality

Athanasios Sourmelidis*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)1399-1421
Number of pages23
JournalThe Ramanujan Journal
Issue number4
Early online date8 Feb 2021
Publication statusPublished - Apr 2022


  • Dirichlet L-functions
  • Hurwitz zeta-functions
  • Universality
  • Weyl sums

ASJC Scopus subject areas

  • Algebra and Number Theory

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