Le théorème d'André-Chudnovsky-Katz « au sens large »
arXiv:1902.07049
Abstract
Siegel's - and -functions were defined in two conjecturally equivalent senses, strict and broad. By taking up and completing a sketch of André, we state and prove the analogue in the broad sense of the André-Chudnovsky-Katz theorem, which is a structure theorem on the -operators in the broad sense (they are differential operators cancelling the -functions in the strict sense). We deduce from that a structure theorem on the -operators in the broad sense, which are differential operators cancelling the -functions in the broad sense. As an application of this last theorem, we give a new proof of a generalization by André of the Siegel-Shidlovskii theorem on the algebraic independence of the values of -functions in the broad sense.
arXiv commentin French. 49 pages