{"docId":1357,"paperId":1357,"url":"https:\/\/hrj.episciences.org\/1357","doi":"10.46298\/hrj.2015.1357","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":48,"name":"Volume 38 - 2015"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01253639","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-01253639v1","dateSubmitted":"2016-01-14 16:08:37","dateAccepted":"2016-01-14 16:08:37","datePublished":"2015-01-01 08:00:00","titles":{"en":"Remarks on the impossibility of a Siegel-Shidlovskii like theorem for G-functions"},"authors":["Rivoal, T"],"abstracts":{"en":"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."},"keywords":[["logarithmic singularity"],["G-functions"],["Siegel-Shidlovskii Theorem"],"Mathematics Subject Classification. 11J91, 34M35.","[MATH] Mathematics [math]"]}