Théorie des nombres
Mesure de Mahler et polylogarithmes
[Mahler measure and polylogarithms]
Comptes Rendus. Mathématique, Volume 338 (2004) no. 10, pp. 747-750.

We prove two new relations between ζ(3),π 2 ln 2,π3L(χ -3 ,2) and some multiple polylogarithms by evaluating twice the logarithmic Mahler measure of the polynomial 1+z1+z2+z3.

L'évaluation de deux façons différentes de la mesure de Mahler du polynôme 1+z1+z2+z3 permet de donner deux nouvelles formules reliant -linéairement ζ(3),π 2 ln 2,π3L(χ -3 ,2) et certaines valeurs de polylogarithmes multiples.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.03.021
Boughzala, Sana 1

1 Université du Centre, IPEIM, rue Ibn Eljazzar, 5019 Monastir, Tunisie
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Boughzala, Sana. Mesure de Mahler et polylogarithmes. Comptes Rendus. Mathématique, Volume 338 (2004) no. 10, pp. 747-750. doi : 10.1016/j.crma.2004.03.021. http://www.numdam.org/articles/10.1016/j.crma.2004.03.021/

[1] Berndt, B. Ramanujan's Notebooks, Springer, 1989

[2] Borwein, J.M.; Bradley, D.M.; Broadhurst, D.J.; Lisonĕk, P. Special values of polylogarithms, Trans. Amer. Math. Soc., Volume 353 (2001) no. 3, pp. 907-941

[3] Boyd, D.W. Speculations concerning the range of Mahler's measure, Canad. Math. Bull., Volume 24 (1981), pp. 453-469

[4] Lewin, L. Polylogarithms and Associated Functions, North-Holland, New York, 1981

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