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SUMMARY:GAAG seminar - On G-functions of differential order 2
DTSTART:20250509T141500
DTEND:20250509T160000
DTSTAMP:20260504T200346Z
UID:a58b9e69096bccc063ea375ed22beef68c93e7b343a0900bbaef9d9d
CATEGORIES:Conferences - Seminars
DESCRIPTION:Javier Fresan (Institut de mathématiques de Jussieu)\nG-funct
 ions are power series that solve a linear differential equation and satisf
 y some growth conditions of arithmetic nature. Those which are solution of
  a differential equation of order 1 are algebraic of a rather particular s
 hape. A rich family of G-functions of differential order 2 is given by alg
 ebraic substitutions of the classical Gauss hypergeometric series. However
 \, I will argue that G-functions of order 2 are infinitely much richer tha
 n those. Indeed\, there exist infinitely many non-equivalent differential 
 equations of order 2 whose solutions include a G-function that is not a po
 lynomial in algebraic substitutions of hypergeometric series. This solves 
 Siegel's problem for G-functions\, as formulated by Fischler and Rivoal\, 
 and answers a question of Krammer in connection to his counterexample to a
  conjecture by Dwork. (Joint work with Josh Lam and Yichen Qin)
LOCATION:GA 3 21 https://plan.epfl.ch/?room==GA%203%2021
STATUS:CONFIRMED
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