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On the Mahler measure of hyperelliptic families

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posted on 2025-05-11, 13:23 authored by Marie José Bertin, Wadim Zudilin
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 y<sup>3</sup>−y+x<sup>3</sup>−x+kxy whose zero loci define elliptic curves for k≠0,±3.

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ARC

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Related Materials

  1. 1.
    DOI - Is published in https://doi.org/10.1007/s40316-016-0068-4
  2. 2.
    ISSN - Is version of https://portal.issn.org/resource/ISSN/2195-4755

Journal title

Annales Mathematiques du Quebec

Volume

41

Issue

1

Pagination

199-211

Publisher

Springer

Language

  • en, English

College/Research Centre

Faculty of Science

School

School of Mathematical and Physical Sciences

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This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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    Keywords

    Mahler measureL-valueelliptic curvehyperelliptic curveelliptic integral

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    CC BY 4.0

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