An explicit formula for the Mahler measure of a family of $3$-variable polynomials

Smyth, Chris J.

An explicit formula for the Mahler measure of a family of

3

-variable polynomials

Smyth, Chris J.

Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 683-700.

Résumé
Abstract

On montre une formule explicite pour la mesure de Mahler du polynôme $a + b x^{- 1} + c y + (a + b x + c y) z$ en termes de dilogarithmes et trilogarithmes.

An explicit formula for the Mahler measure of the $3$ -variable Laurent polynomial $a + b x^{- 1} + c y + (a + b x + c y) z$ is given, in terms of dilogarithms and trilogarithms.

EuDML MR Zbl

@article{JTNB_2002__14_2_683_0,
     author = {Smyth, Chris J.},
     title = {An explicit formula for the {Mahler} measure of a family of $3$-variable polynomials},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {683--700},
     publisher = {Universit\'e Bordeaux I},
     volume = {14},
     number = {2},
     year = {2002},
     mrnumber = {2040701},
     zbl = {1071.11018},
     language = {en},
     url = {http://archive.numdam.org/item/JTNB_2002__14_2_683_0/}
}

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Smyth, Chris J. An explicit formula for the Mahler measure of a family of $3$-variable polynomials. Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 683-700. http://archive.numdam.org/item/JTNB_2002__14_2_683_0/

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