Sharp estimates for the hypergeometric functions related to root systems of type $A$ and of rank $1$
Volume 173 / 2023
Colloquium Mathematicum 173 (2023), 285-309
MSC: Primary 33C67; Secondary 43A90, 53C35.
DOI: 10.4064/cm8893-5-2023
Published online: 6 September 2023
Abstract
We conjecture exact estimates for the Weyl-invariant Opdam–Cherednik hypergeometric functions. We prove the conjecture for the root system $A_n$ and for all rank 1 cases. We provide other evidence that the conjecture might be true in general.
