On the arithmetic properties of complex values of Hecke-Mahler series
classification
🧮 math.NT
keywords
algebraiccomplexhecke-mahlerseriesvaluesarithmeticcharacterisecomplete
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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.
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