Corpus ID: 118935111

Linear independence of linear forms in polylogarithms

  title={Linear independence of linear forms in polylogarithms},
  author={Raffaele Marcovecchio},
  journal={Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze},
  • Raffaele Marcovecchio
  • Published 2006
  • Mathematics
  • Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze
For x ∈ C, |x | < 1, s ∈ N, let Lis(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, Li1(α), Li2(α), . . . 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 Pade approximation problem. Mathematics… Expand
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