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A Case Study for \(\zeta (4)\)

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Transcendence in Algebra, Combinatorics, Geometry and Number Theory (TRANS 2019)

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Abstract

Using symbolic summation tools in the setting of difference rings, we prove a two-parametric identity that relates rational approximations to \(\zeta (4)\).

Date: 17 April 2020. Revised: 22 September 2020

Research partially supported by the Austrian Science Fund (FWF) grants SFB F5006-N15 and F5009-N15 in the framework of the Special Research Program “Algorithmic and Enumerative Combinatorics”.

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Notes

  1. 1.

    In case that the reader does not have access to Mathematica, we supplement the pdf file SchneiderZudilinMMA.pdf (same www-path!) that contains all the calculations in printed form.

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Acknowledgements

This project commenced during the joint visit of the authors in the Max Planck Institute for Mathematics (Bonn) in 2007 and went on during the second author’s visit in the Research Institute for Symbolic Computation (Linz) in February 2020. We thank the staff of these institutes for providing such excellent conditions for research.

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Authors and Affiliations

  1. Research Institute for Symbolic Computation, Johannes Kepler University Linz, Altenberger Str. 69, 4040, Linz, Austria

    Carsten Schneider

  2. Department of Mathematics, IMAPP, Radboud University, PO Box 9010, 6500 GL, Nijmegen, Netherlands

    Wadim Zudilin

Authors
  1. Carsten Schneider
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  2. Wadim Zudilin
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Correspondence to Wadim Zudilin .

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Editors and Affiliations

  1. Inria, Université Paris-Saclay, Palaiseau, France

    Alin Bostan

  2. CNRS, Institut Denis Poisson, Université de Tours,, Tours, France

    Kilian Raschel

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Schneider, C., Zudilin, W. (2021). A Case Study for \(\zeta (4)\). In: Bostan, A., Raschel, K. (eds) Transcendence in Algebra, Combinatorics, Geometry and Number Theory. TRANS 2019. Springer Proceedings in Mathematics & Statistics, vol 373. Springer, Cham. https://doi.org/10.1007/978-3-030-84304-5_17

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