Rivoal, T - Remarks on the impossibility of a Siegel-Shidlovskii like theorem for G-functions

hrj:1357 - Hardy-Ramanujan Journal, January 1, 2015, Volume 38
Remarks on the impossibility of a Siegel-Shidlovskii like theorem for G-functions

Authors: Rivoal, T

The Siegel-Shidlovskii Theorem states that the transcendence degree of the field generated over Q(z) by E-functions solutions of a differential system of order 1 is the same as the transcendence degree of the field generated over Q by the evaluation of these E-functions at non-zero algebraic points (expect possibly at a finite number of them). The analogue of this theorem is false for G-functions and we present conditional and unconditional results showing that any intermediate numerical transcendence degree can be obtained.


Source : oai:HAL:hal-01253639v1
Volume: Volume 38
Published on: January 1, 2015
Submitted on: January 14, 2016
Keywords: logarithmic singularity,G-functions,Siegel-Shidlovskii Theorem, Mathematics Subject Classification. 11J91, 34M35.,[MATH] Mathematics [math]


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