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.
Original language | English |
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Pages (from-to) | 1399-1421 |
Number of pages | 23 |
Journal | The Ramanujan Journal |
Volume | 57 |
Issue number | 4 |
Early online date | 8 Feb 2021 |
DOIs | |
Publication status | Published - Apr 2022 |
Keywords
- Dirichlet L-functions
- Hurwitz zeta-functions
- Universality
- Weyl sums
ASJC Scopus subject areas
- Algebra and Number Theory