A non-hypergeometric E-function

Abstract: With the goal of generalising the theorems of Hermite, Lindemann, and Weierstrass about transcendence of values of the exponential function, Siegel introduced the notion of E-function in his landmark 1929 paper "Über einige Anwendungen diophantischer Approximationen". Hypergeometric functions provide a rich class of E-functions, and Siegel asked whether in fact every E-function is a polynomial expression in hypergeometric E-functions. In a joint work with Javier Fresán, we answer Siegel's question in the negative.

number theory

Audience: researchers in the topic

London number theory seminar

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