Glasnik Matematicki, Vol. 55, No. 2 (2020), 253-265.

DIRICHLET PRODUCT AND THE MULTIPLE DIRICHLET SERIES OVER FUNCTION FIELDS

Yoshinori Hamahata

Department of Applied Mathematics, Okayama University of Science, Ridai-cho 1-1, Okayama, 700-0005, Japan
e-mail: hamahata@xmath.ous.ac.jp


Abstract.   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.

2010 Mathematics Subject Classification.   11R58, 11A25, 11M32, 11M41

Key words and phrases.   Arithmetic function, Dirichlet product, Dirichlet series, zeta function, function field


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https://doi.org/10.3336/gm.55.2.06


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