Tokyo Journal of Mathematics

New Trigonometric Identities and Reciprocity Laws of Generalized Dedekind Sums

Genki SHIBUKAWA

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Abstract

In this paper, we prove new trigonometric identities, which are product-to-sum type formulas for the higher derivatives of the cotangent and cosecant functions. Furthermore, from specializations of our formulas, we derive various known and new reciprocity laws of generalized Dedekind sums.

Article information

Source
Tokyo J. Math., Volume 39, Number 2 (2016), 329-349.

Dates
First available in Project Euclid: 20 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1484903126

Digital Object Identifier
doi:10.3836/tjm/1484903126

Mathematical Reviews number (MathSciNet)
MR3599496

Zentralblatt MATH identifier
06701597

Subjects
Primary: 11L03: Trigonometric and exponential sums, general
Secondary: 11F20: Dedekind eta function, Dedekind sums

Citation

SHIBUKAWA, Genki. New Trigonometric Identities and Reciprocity Laws of Generalized Dedekind Sums. Tokyo J. Math. 39 (2016), no. 2, 329--349. doi:10.3836/tjm/1484903126. https://projecteuclid.org/euclid.tjm/1484903126


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References

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