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Transformation of Some Lambert Series and Cotangent Sums

Author

Listed:
  • Namhoon Kim

    (Department of Mathematics Education, Hongik University, 94 Wausan-ro, Mapo-gu, Seoul 04066, Korea)

Abstract

By considering a contour integral of a cotangent sum, we give a simple derivation of a transformation formula of the series A ( τ , s ) = ∑ n = 1 ∞ σ s − 1 ( n ) e 2 π i n τ for complex s under the action of the modular group on τ in the upper half plane. Some special cases directly give expressions of generalized Dedekind sums as cotangent sums.

Suggested Citation

  • Namhoon Kim, 2019. "Transformation of Some Lambert Series and Cotangent Sums," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:840-:d:266160
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