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arXiv · 1506.01809

Periodic analogues of Dedekind sums and transformation formulas of Eisenstein series

M. Cihat Dağlı·Mümün Can
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Abstract

In this paper, a transformation formula under modular substitutions is derived for a large class of generalized Eisenstein series. Appearing in the transformation formulae are generalizations of Dedekind sums involving the periodic Bernoulli function. Reciprocity theorems are proved for these Dedekind sums. Furthermore, as an application of the transformation formulae, relations between various infinite series and evaluations of several infinite series are deduced. Finally, we consider these sums for some special cases.

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M. Cihat Dağlı, Mümün Can. 2016-01-06. Periodic analogues of Dedekind sums and transformation formulas of Eisenstein series. https://doi.org/10.1007/s11139-016-9808-y

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