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arXiv · 2512.02428

Effective hybrid joint universality for Dirichlet $L$-functions and its application

Keita Nakai
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Abstract

In 2003, Garunk\v{s}tis provided a lower bound for the lower density of the universality theorem for the Riemann zeta-function. In this paper, we generalize this result for the hybrid joint universality theorem for Dirichlet $L$-functions whose moduli are prime numbers. Furthermore, by its application, we estimate a lower bound of the lower density of the universality theorem for Hurwitz zeta-functions with rational parameters.

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Keita Nakai. 2025-12-02. Effective hybrid joint universality for Dirichlet $L$-functions and its application. https://arxiv.org/abs/2512.02428

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