On superzeta functions of the first kind on function fields
Kajtaz H. Bllaca\,^1, Jawher Khmiri\,^2, Kamel Mazhouda\,^3 and Bouchaïb Sodaïgui\,^4
\,^{1}Department of Mathematics, University of Prishtina, Mother Theresa, no. 5, 10000 Prishtina, Kosovo
\,^{2}University of Monastir, Faculty of Science of Monastir, 5000 Monastir, Tunisia
\,^{3}University of Sousse, Higher Institute of Applied Sciences and Technology, 4003 Sousse, Tunisia
\,^{4}Univ. Polytechnique Hauts-De-France, INSA Hauts-De-France, FR CNRS 2037,
CERAMATHS, F-59313 Valenciennes, France
Pages 28-37 | Received 12 June 2024, Accepted 05 November 2024, Published 10 July 2025
Abstract
In a recent article [2], we studied the superzeta functions on function fields. In this paper, we continue our investigation on the superzeta functions of the first kind. We prove results concerning their link with the Euler-Stieltjes constants and we give formulas for the r-depth regularized product of their zeros.
Keywords: Function fields, Superzeta functions, Riemann hypothesis, Li coefficients.
MSC numbers: Primary 11M41; Secondary 11M38.
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