Algebraicity of hypergeometric functions with arbitrary parameters
Classical Analysis and ODEs
2024-05-16 v3 Combinatorics
Abstract
We provide a complete classification of the algebraicity of (generalized) hypergeometric functions with no restriction on the set of their parameters. Our characterization relies on the interlacing criteria of Christol (1987) and Beukers-Heckman (1989) for globally bounded and algebraic hypergeometric functions, however in a more general setting which allows arbitrary complex parameters with possibly integral differences. We also showcase the adapted criterion on a variety of different examples.
Cite
@article{arxiv.2308.12855,
title = {Algebraicity of hypergeometric functions with arbitrary parameters},
author = {Florian Fürnsinn and Sergey Yurkevich},
journal= {arXiv preprint arXiv:2308.12855},
year = {2024}
}
Comments
revised version, 21 pages, to appear in the Bulletin of the London Mathematical Society