10.46298/hrj.2015.1357
Rivoal, T
T
Rivoal
Remarks on the impossibility of a Siegel-Shidlovskii like theorem for G-functions
episciences.org
2015
logarithmic singularity
G-functions
Siegel-Shidlovskii Theorem
Mathematics Subject Classification. 11J91, 34M35.
[MATH] Mathematics [math]
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Journal article
https://hrj.episciences.org/1357
https://hal.archives-ouvertes.fr/hal-01253639v1
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Hardy-Ramanujan Journal ; Volume 38 - 2015
International audience
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.