1Hachinohe National College of Technology, Uwanotai, Tamonoki, Hachinoheshi, Aomoriken, Japan
Turkish Journal of Analysis and Number Theory.
2015,
Vol. 3 No. 5, 140-144
DOI: 10.12691/tjant-3-5-5
Copyright © 2015 Science and Education PublishingCite this paper: Takahiro Wakasa. An Explicit upper Bound of the Argument of Dirichlet
L-functions on the Generalized Riemann Hypothesis.
Turkish Journal of Analysis and Number Theory. 2015; 3(5):140-144. doi: 10.12691/tjant-3-5-5.
Correspondence to: Takahiro Wakasa, Hachinohe National College of Technology, Uwanotai, Tamonoki, Hachinoheshi, Aomoriken, Japan. Email:
wakasa-g@hachinohe-ct.ac.jpAbstract
We prove an explicit upper bound of the function
, defined by the argument of Dirichlet
L-functions attached to a primitive Dirichlet character
(mod
q > 1). An explicit upper bound of the function
S(
t), defined by the argument of the Riemann zeta-function, have been obtained by A. Fujii [1]. Our result is obtained by applying the idea of Fujii's result on
S(
t). The constant part of the explicit upper bound of
in this paper does not depend on
. Our proof does not cover the case
q = 1 and indeed gives a better bound than the one of Fujii that covers the case
q = 1.
Keywords