On a Class of Hypergeometric Diagonals

2020/08/28 by Alin Bostan, Sergey Yurkevich, Bostan, Alin +1
Mathematics · #33D15 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:33D15

paper · pdf · doi:10.48550/arxiv.2008.12809

To appear in Proceedings of the AMS

arxiv created 2021/06/05 · arxiv updated 2021/06/08

Abstract

We prove that the diagonal of any finite product of algebraic functions of the form (1-x₁-…-x_n)^R, R∈ℚ, 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 [AKM2020, §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 [AKM2020], our proof is completely elementary and does not require any algorithmic help.

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