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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