On the Mahler measure of hyperelliptic families

被引：6

作者：

Bertin M.J. ^{[1
]}

Zudilin W. ^{[2
,3
]}

机构：

[1] Institut de Mathématiques, Université Pierre et Marie Curie (Paris 6), 4 Place Jussieu, Paris

[2] Max-Planck-Institut für Mathematik, Vivatsgasse 7, Bonn

[3] School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, 2308, NSW

来源：

Annales mathématiques du Québec | 2017年 / 41卷 / 1期

基金：

澳大利亚研究理事会;

关键词：

Elliptic curve; Elliptic integral; Hyperelliptic curve; L-value; Mahler measure;

D O I：

10.1007/s40316-016-0068-4

中图分类号：

学科分类号：

摘要：

We prove Boyd’s “unexpected coincidence” of the Mahler measures for two families of two-variate polynomials defining curves of genus 2. We further equate the same measures to the Mahler measures of polynomials y3- y+ x3- x+ kxy whose zero loci define elliptic curves for k≠ 0 , ± 3. © 2016, The Author(s).

引用

页码：199 / 211

页数：12

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