@article{tjant2015355,
author={Wakasa, Takahiro},
title={An Explicit upper Bound of the Argument of Dirichlet <i>L</i>-functions on the Generalized Riemann Hypothesis},
journal={Turkish Journal of Analysis and Number Theory},
volume={3},
number={5},
pages={140--144},
year={2015},
url={http://pubs.sciepub.com/tjant/3/5/5},
issn={2333-1232},
abstract={We prove an explicit upper bound of the function <img src=image/abs1.png></img>, defined by the argument of Dirichlet <i>L</i>-functions attached to a primitive Dirichlet character <img src=image/abs2.png></img><i> </i>(mod <i>q > </i>1). An explicit upper bound of the function <i>S</i>(<i>t</i>), 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 <i>S</i>(<i>t</i>). The constant part of the explicit upper bound of <img src=image/abs3.png></img> in this paper does not depend on <img src=image/abs4.png></img>. Our proof does not cover the case <i>q </i>= 1 and indeed gives a better bound than the one of Fujii that covers the case <i>q </i>= 1.},
doi={10.12691/tjant-3-5-5}
publisher={Science and Education Publishing}
}