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arXiv · 2508.17701

Detecting zeros of Dirichlet $L$-functions via the Riemann zeta-function

Masatoshi Suzuki
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Abstract

Assuming the Riemann hypothesis, we show that a certain vertical distribution of the nontrivial zeros of the Riemann zeta-function is equivalent to the generalized Riemann hypothesis for Dirichlet $L$-functions. Furthermore, under both the Riemann hypothesis and the generalized Riemann hypothesis, we show that the nontrivial zeros of Dirichlet $L$-functions can be detected through those of the Riemann zeta-function.

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Masatoshi Suzuki. 2025-08-25. Detecting zeros of Dirichlet $L$-functions via the Riemann zeta-function. https://arxiv.org/abs/2508.17701

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