Abstract: The classification of algebraic hypergeometric functions is a classical problem and early results go back to Schwarz in the late 19th century. In this talk I will give an overview on the history of the question and then present a complete criterion for algebraicity of (generalized) hypergeometric functions with no restriction on their set of parameters. It relies on the interlacing criteria of Christol (1986) and Beukers-Heckman (1989), which I will present as well, but allows arbitrary complex parameters with possibly integral differences. I will showcase the result on various examples with connections to combinatorics and explain how it can be useful in the classification of generating functions. This talk is based on joint work with Sergey Yurkevich.
Algebraicity of Hypergeometric Functions with Arbitrary Parameters
23.01.2024 15:15 - 16:45
Organiser:
I. Fischer (U Wien), M. Schlosser (U. Wien)
Location: