20230719 
14:0014:45 
20230719,14:0014:45  LR3 (A31a 2F) 
0719 Afternoon Math Lecture Room 3 (A31a 2F)

Speaker 
Efunctions and Geometry Siegel introduced the notion of Efunction in a landmark 1929 paper with the goal of generalising the HermiteLindemannWeierstrass theorem on the transcendence of the values of the exponential function at algebraic numbers. Efunctions are power series with algebraic coefficients that are solutions of a linear differential equation and satisfy some growth conditions of arithmetic nature. Besides the exponential function, examples include Bessel functions and a rich family of hypergeometric series. Siegel asked whether all Efunctions are polynomial expressions in these hypergeometric series. I explain why the answer to Siegel's question is negative, and then try to amend it by describing how Efunctions arise from geometry in the form of "exponential period functions" and why it might seem reasonable, in the light of other conjectures, to expect that all Efunctions are of this kind.
