An explicit upper bound of the argument of Dirichlet $L$-functions on the generalized Riemann hypothesis

Takahiro Wakasa

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arXiv · 1406.2803

An explicit upper bound of the argument of Dirichlet $L$-functions on the generalized Riemann hypothesis

Takahiro Wakasa

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Abstract

We prove an explicit upper bound of the function $S(t,\chi)$, defined by the argument of Dirichlet $L$-functions. An explicit upper bound of the function $S_1(t)$, defined by the integral of the argument of the Riemann zeta-function, have already been obtained by A. Fujii. Our result is obtained by applying an idea of Fujii's result on $S_1(t)$. The constant part of the explicit upper bound of $S(t,\chi)$ in this paper does not depend on a primitive Dirichlet character $\chi\pmod {q>1}$.

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Takahiro Wakasa. 2014-06-11. An explicit upper bound of the argument of Dirichlet $L$-functions on the generalized Riemann hypothesis. https://arxiv.org/abs/1406.2803

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