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Finite trigonometric sums arising from Ramanujan’s theta functions

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Abstract

Two classes of finite trigonometric sums, each involving only sines, are evaluated in closed form. The previous and original proofs arise from Ramanujan’s theta functions and modular equations.

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Acknowledgements

The authors are grateful to the anonymous referees for very careful readings of our manuscript and for their helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL, 61801, USA

    Bruce C. Berndt & Alexandru Zaharescu

  2. Department of Mathematics, and Institute of Pure and Applied Mathematics, Jeonbuk National University, 567 Baekje-daero, Jeonju-si, Jeollabuk-do, 54896, Republic of Korea

    Sun Kim

  3. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700, Bucharest, Romania

    Alexandru Zaharescu

Authors
  1. Bruce C. Berndt
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  2. Sun Kim
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  3. Alexandru Zaharescu
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Correspondence to Sun Kim.

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The second author’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2023-00240168).

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Berndt, B.C., Kim, S. & Zaharescu, A. Finite trigonometric sums arising from Ramanujan’s theta functions. Ramanujan J 63, 673–685 (2024). https://doi.org/10.1007/s11139-023-00778-2

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  • DOI: https://doi.org/10.1007/s11139-023-00778-2

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