Abstract
We derive an explicit expression for an inverse power series over the gaps values of numerical semigroups generated by two integers. It implies the multiplication theorem for the Hurwitz zeta function \(\zeta (n,q)\).
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References
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Acknowledgements
The main part of the paper was written during the stay of one of the authors (LGF) at the School of Mathematics and Statistics of Wuhan University and its hospitality is highly appreciated. The research was supported in part (LGF) by the Kamea Fellowship and JSPS KAKENHI Grant Number 18K13400, and was in part conducted (AIS) under RIKEN Special Postdoctoral Researcher program.
The present paper is an extended version of the preprint [6] posted on arXiv.org.
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Fel, L.G., Komatsu, T., Suriajaya, A.I. (2021). A Sum of Negative Degrees of the Gaps Values in Two-Generated Numerical Semigroups and Identities for the Hurwitz Zeta Function. In: Nathanson, M.B. (eds) Combinatorial and Additive Number Theory IV. CANT 2020. Springer Proceedings in Mathematics & Statistics, vol 347. Springer, Cham. https://doi.org/10.1007/978-3-030-67996-5_8
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