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SUMMARY:A non-hypergeometric E-function
DTSTART;VALUE=DATE-TIME:20221207T141500
DTEND;VALUE=DATE-TIME:20221207T151500
UID:a87b4c22f2230f0db5745bd83dd77b98ef65afb32add3e3138debf48
CATEGORIES:Conferences - Seminars
DESCRIPTION:Javier Fresàn (Ecole Polytechnique\, Palaiseau\, France)\nIn
a landmark 1929 paper\, Siegel introduced the class of E-functions with th
e goal of generalising the transcendence theorems for the values of the ex
ponential. E-functions are power series with algebraic coefficients subjec
t to certain growth conditions of arithmetic nature that satisfy a linear
differential equation. Besides the exponential\, examples include Bessel f
unctions and a rich family of hypergeometric series. Siegel asked whether
all E-functions are polynomial expressions in these hypergeometric series.
I will explain why the answer is negative and a possible amendment to Sie
gel's question in the form "all E-functions come from exponential motives"
. This is a joint work with P. Jossen.
LOCATION:GR A3 31 https://plan.epfl.ch/?room==GR%20A3%2031
STATUS:CONFIRMED
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