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An elliptic analogue of a theorem of Hecke

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Abstract

We revisit the classical theorem of Euler regarding special values of the Riemann zeta function as well as Hecke’s generalization of this to Dirichlet’s \(L\)-functions and derive an elliptic analogue. We also discuss transcendence questions that arise from this analogue.

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Acknowledgments

We are grateful to Purusottam Rath, Michel Waldschmidt and the referee for their comments on a previous version of this paper.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Queen’s University, Kingston, ON, K7L 3N6, Canada

    M. Ram Murty & Akshaa Vatwani

Authors
  1. M. Ram Murty
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  2. Akshaa Vatwani
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Corresponding author

Correspondence to M. Ram Murty.

Additional information

Dedicated to the memory of Marvin Knopp, with respect and admiration.

Research of the second author was supported by an NSERC Discovery Grant.

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Ram Murty, M., Vatwani, A. An elliptic analogue of a theorem of Hecke. Ramanujan J 41, 171–182 (2016). https://doi.org/10.1007/s11139-014-9597-0

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  • DOI: https://doi.org/10.1007/s11139-014-9597-0

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