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

Takahiro Wakasa

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

机译：广义黎曼假设上Dirichlet L函数的参数的显式上界

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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.

机译：我们证明了该函数的显式上限，该上限由附加到原始Dirichlet字符（mod q> 1）的Dirichlet L函数的自变量定义。由R.mann zeta函数的自变量定义的函数S（t）的明确上限已由A. Fujii [1]获得。我们的结果是通过将Fujii的结果应用于S（t）来获得的。本文明确上限的常数部分不依赖于。我们的证明没有涵盖q = 1的情况，并且确实给出了比涵盖q = 1的Fujii更好的边界。

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《Turkish Journal of Analysis and Number Theory》 |2015年第5期|共5页
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Takahiro Wakasa;
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中图分类数学;
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An Explicit upper Bound of the Argument of Dirichlet L-functions on the Generalized Riemann Hypothesis

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