eng
episciences.org
Hardy-Ramanujan Journal
2804-7370
2015-01-01
Volume 38 - 2015
10.46298/hrj.2015.1357
1357
journal article
Remarks on the impossibility of a Siegel-Shidlovskii like theorem for G-functions
T Rivoal
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.
https://hrj.episciences.org/1357/pdf
logarithmic singularity
G-functions
Siegel-Shidlovskii Theorem
Mathematics Subject Classification. 11J91, 34M35.
[MATH] Mathematics [math]