An Explicit upper Bound of the Argument of Dirichlet L-functions on the Generalized Riemann Hypothesis

Takahiro Wakasa^1,

¹Hachinohe National College of Technology, Uwanotai, Tamonoki, Hachinoheshi, Aomoriken, Japan

Cite 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

Abstract

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:
Dirichlet L-functions

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References:

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