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Modular forms and q-analogues of modified double zeta values

Abstract

We present explicit formulas for Hecke eigenforms as linear combinations of q-analogues of modified double zeta values. As an application, we obtain period polynomial relations and sum formulas for these modified double zeta values. These relations have similar shapes as the period polynomial relations of Gangl, Kaneko, and Zagier and the usual sum formulas for classical double zeta values.

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Acknowledgements

The author would like to thank Ulf Kühn, Nils Matthes and the referee for a lot fruitful comments and corrections.

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Correspondence to Henrik Bachmann.

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Communicated by Jens Funke.

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Bachmann, H. Modular forms and q-analogues of modified double zeta values. Abh. Math. Semin. Univ. Hambg. 90, 201–213 (2020). https://doi.org/10.1007/s12188-020-00227-7

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Keywords

  • Modular forms
  • Double zeta values
  • Period polynomials
  • Hecke operators

Mathematics Subject Classification

  • Primary 11F11
  • 11M32;
  • Secondary 11F67