Equations for Mahler measure and isogenies
Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 2, p. 387-399

We study some functional equations between Mahler measures of genus-one curves in terms of isogenies between the curves. These equations have the potential to establish relationships between Mahler measure and especial values of L-functions. These notes are based on a talk that the author gave at the “Cuartas Jornadas de Teoría de Números”, Bilbao, 2011.

Nous étudions quelques équations fonctionnelles de la mesure de Mahler de familles de courbes de genre 1 en utilisant des isogénies entre les courbes. Ces équations ont le potentiel d’aider à trouver des relations entre la mesure de Mahler et des valeurs spéciales de fonctions L. Ces notes sont inspirées d’une présentation de l’auteure aux Cuartas Jornadas de Teoría de Números, à Bilbao, 2011.

@article{JTNB_2013__25_2_387_0,
     author = {Lal\'\i n, Matilde N.},
     title = {Equations for Mahler measure and isogenies},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {25},
     number = {2},
     year = {2013},
     pages = {387-399},
     doi = {10.5802/jtnb.841},
     mrnumber = {3228313},
     zbl = {1283.11095},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2013__25_2_387_0}
}
Lalín, Matilde N. Equations for Mahler measure and isogenies. Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 2, pp. 387-399. doi : 10.5802/jtnb.841. http://www.numdam.org/item/JTNB_2013__25_2_387_0/

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