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

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  • Published: 21 December 2015
  • volume 1, Article number: 27 (2015)
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A correspondence of modular forms and applications to values of L-series
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  • Nikolaos Diamantis1,
  • Michael Neururer1 &
  • Fredrik Strömberg1 
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  • 3 Citations

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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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References

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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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Authors and Affiliations

  1. University of Nottingham, Nottingham, UK

    Nikolaos Diamantis, Michael Neururer & Fredrik Strömberg

Authors
  1. Nikolaos Diamantis
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  2. Michael Neururer
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  3. Fredrik Strömberg
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Corresponding author

Correspondence to Nikolaos Diamantis.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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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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  • Received: 24 April 2015

  • Accepted: 27 October 2015

  • Published: 21 December 2015

  • DOI: https://doi.org/10.1007/s40993-015-0029-z

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Keywords

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