Les nombres de Tamagawa locaux et la conjecture de Bloch et Kato pour les motifs Q(m) sur un corps abélien
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Denis Benois, Thong Nguyen Quang Do (2002)
Annales scientifiques de l'École Normale Supérieure
Raffaele Marcovecchio (2006)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
For , , , let be the -th polylogarithm of . We prove that for any non-zero algebraic number such that , the -vector space spanned by has infinite dimension. This result extends a previous one by Rivoal for rational . 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.
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