Speaker: Javier Fresán
Date: 10:30 13/11/2020
Title: E-functions and (hyper)geometry
Abstract:  In a landmark 1929 paper, Siegel introduced the class of E-functions with the goal of generalising the transcendence 
theorems for the values of the exponential. E-functions are power series with algebraic coefficients subject to certain growth 
conditions that satisfy a linear differential equation. Besides the exponential, examples include Bessel functions and a rich 
family of hypergeometric series. Siegel asked whether all E-functions are polynomial expressions in these hypergeometrics. 
In a recent wok, Fischler and Rivoal showed that a positive answer to Siegel’s question would contradict Grothendieck’s period 
conjecture. In this talk, I will sketch an unconditional approach to the question based on differential Galois theory. 
This is a joint work with Peter Jossen.