• Corpus ID: 19020213

Multiple zeta values, Pad\'e approximation and Vasilyev's conjecture

@article{Fischler2013MultipleZV,
  title={Multiple zeta values, Pad\'e approximation and Vasilyev's conjecture},
  author={St{\'e}phane Fischler and Tanguy Rivoal},
  journal={arXiv: Number Theory},
  year={2013}
}
Sorokin gave in 1996 a new proof that pi is transcendental. It is based on a simultaneous Pad\'e approximation problem involving certain multiple polylogarithms, which evaluated at the point 1 are multiple zeta values equal to powers of pi. In this paper we construct a Pad\'e approximation problem of the same flavour, and prove that it has a unique solution up to proportionality. At the point 1, this provides a rational linear combination of 1 and multiple zeta values in an extended sense that… 
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