On the arithmetic properties of complex values of Hecke-Mahler series. I. The rank one case
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 3, pp. 329-374.

Here we characterise, in a complete and explicit way, the relations of algebraic dependence over ℚ of complex values of Hecke-Mahler series taken at algebraic points u ̲ 1 ,...,u ̲ m of the multiplicative group 𝔾 m 2 (ℂ), under a technical hypothesis that a certain sub-module of 𝔾 m 2 (ℂ) generated by the u ̲ i ’s has rank one (rank one hypothesis). This is the first part of a work, announced in [Pel1], whose main objective is completely to solve a general problem on the algebraic independence of values of these series.

Classification : 11J85, 11J91 
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     author = {Pellarin, Federico},
     title = {On the arithmetic properties of complex values of {Hecke-Mahler} series. {I.} {The} rank one case},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 5},
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Pellarin, Federico. On the arithmetic properties of complex values of Hecke-Mahler series. I. The rank one case. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 3, pp. 329-374. http://www.numdam.org/item/ASNSP_2006_5_5_3_329_0/

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