Abstract
Since Euler, values of various zeta functions have long attracted a lot of mathematicians. In computer algebra community, Apéry’s proof of the irrationality of ζ(3) is well known. In this paper, we are concerned with the “multiple zeta value (MZV)”. More than fifteen years ago, D. Zagier gave a conjecture on MZVs based on numerical computations on PARI. Since then there have been various derived conjectures and two kinds of efforts for attacking them: one is a mathematical proof and another one is a computational experiment to get more confidence to verify a conjecture. We have checked one of these conjectures up to weight k = 20, which will be explained later, with Risa/Asir function for non-commutative polynomials and special parallel programs of linear algebra designed for this purpose.
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Kaneko, M., Noro, M., Tsurumaki, K. (2008). On a Conjecture for the Dimension of the Space of the Multiple Zeta Values. In: Stillman, M., Verschelde, J., Takayama, N. (eds) Software for Algebraic Geometry. The IMA Volumes in Mathematics and its Applications, vol 148. Springer, New York, NY. https://doi.org/10.1007/978-0-387-78133-4_4
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DOI: https://doi.org/10.1007/978-0-387-78133-4_4
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