On the arithmetic properties of complex values of Hecke-Mahler series.

Federico Pellarin (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

Here we characterise in a complete and explicit way the relations of algebraic dependence over $\QQ$ of complex values of Hecke-Mahler series taken at algebraic points of the multiplicative group $\GG_m^2(\CC)$. Our result contains previous theorems by Loxton and van der Poorten, Mahler, and Masser.

Mots clés: Hecke-Mahler series; algebraic independence; real multiplication

Domaines: Théorie des nombres [math.NT]

Federico Pellarin. On the arithmetic properties of complex values of Hecke-Mahler series.. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2006, V (5), pp.329-374. ⟨hal-00002262⟩