Yoshinori Hamahata
Abstract
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We define the Dirichlet product for multiple arithmetic functions over function fields and consider the ring of the multiple Dirichlet series over function fields. We apply our results to absolutely convergent multiple Dirichlet series and obtain some zero-free regions for them.
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We define the Dirichlet product for multiple arithmetic functions over function fields and consider the ring of the multiple Dirichlet series over function fields. We apply our results to absolutely convergent multiple Dirichlet series and obtain some zero-free regions for them.
Key concepts: Dirichlet series, General Dirichlet series, Mathematics, Dirichlet kernel, Dirichlet L-function, Dirichlet's energy, Generalized Dirichlet distribution, Dirichlet conditions