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On a Class of Hypergeometric Diagonals

Abstract : We prove that the diagonal of any finite product of algebraic functions of the form $ {(1-x_1- \dots -x_n)^R}, \; R\in\mathbb{Q}$, is a generalized hypergeometric function, and we provide 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 [AKM, §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 [AKM], our proof is completely elementary and does not require any algorithmic help.
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https://hal.inria.fr/hal-03084672
Contributor : Alin Bostan Connect in order to contact the contributor
Submitted on : Monday, December 21, 2020 - 11:58:21 AM
Last modification on : Monday, May 3, 2021 - 10:22:20 PM

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2008.12809.pdf
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  • HAL Id : hal-03084672, version 1
  • ARXIV : 2008.12809

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Alin Bostan, Sergey Yurkevich. On a Class of Hypergeometric Diagonals. Proceedings of the American Mathematical Society, American Mathematical Society, In press. ⟨hal-03084672⟩

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