[Mahler measure and polylogarithms]
We prove two new relations between 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 et certaines valeurs de polylogarithmes multiples.
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Sana Boughzala 1
@article{CRMATH_2004__338_10_747_0, author = {Sana Boughzala}, title = {Mesure de {Mahler} et polylogarithmes}, journal = {Comptes Rendus. Math\'ematique}, pages = {747--750}, publisher = {Elsevier}, volume = {338}, number = {10}, year = {2004}, doi = {10.1016/j.crma.2004.03.021}, language = {fr}, }
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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.03.021/
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[4] Polylogarithms and Associated Functions, North-Holland, New York, 1981
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