Comptes Rendus
no. 10
Théorie des nombres
Mesure de Mahler et polylogarithmes
[Mahler measure and polylogarithms]
Presented by: Jean-Pierre Serre
Sana Boughzala1
1Université du Centre, IPEIM, rue Ibn Eljazzar, 5019 Monastir, Tunisie
Comptes Rendus. Mathématique, Volume 338 (2004) no. 10, pp. 747-750

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

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.03.021

Sana Boughzala  1

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

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

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

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

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

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