Cotangent zeta functions in function fields

We introduce and study an analogue of the cotangent zeta function in the function fields setting. We establish a relation of our newly introduced zeta function to the Apostol–Dedekind sum, and then prove a functional equation for our function. Finally, we compute special values of the cotangent zeta...

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Veröffentlicht in:	The Ramanujan journal 2017, Vol.42 (1), p.15-27
1. Verfasser:	Hamahata, Yoshinori
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorics Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Mathematics Mathematics and Statistics Number Theory
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We introduce and study an analogue of the cotangent zeta function in the function fields setting. We establish a relation of our newly introduced zeta function to the Apostol–Dedekind sum, and then prove a functional equation for our function. Finally, we compute special values of the cotangent zeta function at quadratic irrationals.
ISSN:	1382-4090 1572-9303
DOI:	10.1007/s11139-016-9816-y