Zeros of the first derivative of Dirichlet L-functions

Hirotaka Akatsuka, Ade Irma Suriajaya

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1 Citation (Scopus)

Abstract

Yıldırım has classified zeros of the derivatives of Dirichlet L-functions into trivial zeros, nontrivial zeros and vagrant zeros. In this paper we remove the possibility of vagrant zeros for L (s,χ) when the conductors are large to some extent. Then we improve asymptotic formulas for the number of zeros of L (s,χ) in {s∈C:Re(s)>0,|Im(s)|≤T}. We also establish analogues of Speiser's theorem, which characterize the generalized Riemann hypothesis for L(s,χ) in terms of zeros of L (s,χ), when the conductor is large.

Original languageEnglish
Pages (from-to)300-329
Number of pages30
JournalJournal of Number Theory
Volume184
DOIs
Publication statusPublished - Mar 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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