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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a class of hypergeometric diagonals
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by Alin Bostan and Sergey Yurkevich PDF
Proc. Amer. Math. Soc. 150 (2022), 1071-1087 Request permission


We prove that the diagonal of any finite product of algebraic functions of the form \begin{align*} {(1-x_1- \dots -x_n)^R}, \qquad R\in \mathbb {Q}, \end{align*} is a generalized hypergeometric function, and we provide an explicit description of its parameters. The particular case $(1-x-y)^R/(1-x-y-z)$ corresponds to the main identity of Abdelaziz, Koutschan and Maillard in [J. Phys. A 53 (2020), 205201, 16 pp., §3.2]. Our result is useful in both directions: on the one hand it shows that Christol’s conjecture holds true for a large class of hypergeometric functions, on the other hand it allows for a very explicit and general viewpoint on the diagonals of algebraic functions of the type above. Finally, in contrast to the approach of Abdelaziz, Koutschan and Maillard, our proof is completely elementary and does not require any algorithmic help.
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Additional Information
  • Alin Bostan
  • Affiliation: Inria, Université Paris-Saclay, 1 rue Honoré d’Estienne d’Orves, 91120 Palaiseau, France
  • MR Author ID: 725685
  • ORCID: 0000-0003-3798-9281
  • Email:
  • Sergey Yurkevich
  • Affiliation: Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria
  • Email:
  • Received by editor(s): September 6, 2020
  • Received by editor(s) in revised form: May 24, 2021
  • Published electronically: January 5, 2022
  • Additional Notes: The first author was supported in part by DeRerumNatura ANR-19-CE40-0018.
    The second author was supported by the Austrian Science Fund (FWF): P-31338.
  • Communicated by: Rachel Pries
  • © Copyright 2022 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 150 (2022), 1071-1087
  • MSC (2020): Primary 30B10, 33C20; Secondary 13F25, 11R58
  • DOI:
  • MathSciNet review: 4375704