Linear independence of linear forms in polylogarithms

Marcovecchio, Raffaele

Marcovecchio, Raffaele

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 1, pp. 1-11.

Résumé

For $x \in ℂ$ , $| x | < 1$ , $s \in ℕ$ , let ${Li}_{s} (x)$ be the $s$ -th polylogarithm of $x$ . We prove that for any non-zero algebraic number $α$ such that $| α | < 1$ , the $ℚ (α)$ -vector space spanned by $1, {Li}_{1} (α), {Li}_{2} (α), \dots$ has infinite dimension. This result extends a previous one by Rivoal for rational $α$ . The main tool is a method introduced by Fischler and Rivoal, which shows the coefficients of the polylogarithms in the relevant series to be the unique solution of a suitable Padé approximation problem.

MR Zbl | 2 citations dans Numdam

Classification : 11J72, 11J17, 11J91, 33C20

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Marcovecchio, Raffaele. Linear independence of linear forms in polylogarithms. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 1, pp. 1-11. http://archive.numdam.org/item/ASNSP_2006_5_5_1_1_0/

Bibliographie
Cité par

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