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arXiv · 1601.07583

On the Mahler measure of hyperelliptic families

Marie José Bertin·Wadim Zudilin
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Abstract

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 $y^3-y+x^3-x+kxy$ whose zero loci define elliptic curves for $k\ne0,\pm3$.

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BibTeXRIS

Marie José Bertin, Wadim Zudilin. 2016-01-27. On the Mahler measure of hyperelliptic families. https://doi.org/10.1007/s40316-016-0068-4

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