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arXiv · 2201.10771

Estimates for $L$-functions in the critical strip under GRH with effective applications

Aleksander Simonič
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Abstract

Assuming the Generalized Riemann Hypothesis, we provide explicit upper bounds for moduli of $\log{\mathcal{L}(s)}$ and $\mathcal{L}'(s)/\mathcal{L}(s)$ in the neighbourhood of the 1-line when $\mathcal{L}(s)$ are the Riemann, Dirichlet and Dedekind zeta-functions. To do this, we generalize Littlewood's well known conditional result to functions in the Selberg class with a polynomial Euler product, for which we also establish a suitable convexity estimate. As an application we provide conditional and effective estimate for the Mertens function.

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Aleksander Simonič. 2022-01-26. Estimates for $L$-functions in the critical strip under GRH with effective applications. https://arxiv.org/abs/2201.10771

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