TY - JOUR
T1 - Zeros of the first derivative of Dirichlet L-functions
AU - Akatsuka, Hirotaka
AU - Suriajaya, Ade Irma
N1 - Funding Information:
The second named author was in part supported by JSPS KAKENHI Grant Number 15J02325 .
Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2018/3
Y1 - 2018/3
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jnt.2017.08.023
DO - 10.1016/j.jnt.2017.08.023
M3 - Article
AN - SCOPUS:85030570659
SN - 0022-314X
VL - 184
SP - 300
EP - 329
JO - Journal of Number Theory
JF - Journal of Number Theory
ER -