Here we characterise, in a complete and explicit way, the relations of algebraic dependence over of complex values of Hecke-Mahler series taken at algebraic points of the multiplicative group , under a technical hypothesis that a certain sub-module of generated by the ’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.
@article{ASNSP_2006_5_5_3_329_0, 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}, pages = {329--374}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 5}, number = {3}, year = {2006}, zbl = {1116.11057}, mrnumber = {2274783}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2006_5_5_3_329_0/} }
TY - JOUR AU - Pellarin, Federico TI - On the arithmetic properties of complex values of Hecke-Mahler series. I. The rank one case JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2006 DA - 2006/// SP - 329 EP - 374 VL - Ser. 5, 5 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2006_5_5_3_329_0/ UR - https://zbmath.org/?q=an%3A1116.11057 UR - https://www.ams.org/mathscinet-getitem?mr=2274783 LA - en ID - ASNSP_2006_5_5_3_329_0 ER -
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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