A correspondence of modular forms and applications to values of L-series

Abstract

A interpretation of the Rogers–Zudilin approach to the Boyd conjectures is established. This is based on a correspondence of modular forms which is of independent interest. We use the reinterpretation for two applications to values of L-series and values of their derivatives.

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Acknowledgements

We are grateful to Kathrin Bringmann for drawing our attention to [7] and for many interesting discussions and to Don Zagier for many valuable comments on an early form of the note. We also thank Francois Brunault for reading carefully the submitted version of the paper and for offering very useful feedback. Finally we would like to thank the referee for very helpful comments that improved the exposition of the paper.

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Correspondence to Nikolaos Diamantis.

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Diamantis, N., Neururer, M. & Strömberg, F. A correspondence of modular forms and applications to values of L-series. Res. number theory 1, 27 (2015). https://doi.org/10.1007/s40993-015-0029-z

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Keywords

  • L-functions
  • Derivatives of L-functions
  • Eisenstein series