## On the Mahler measure of hyperelliptic families.(English. French summary)Zbl 1434.11211

Summary: 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 $$k\neq 0,\pm 3$$.

### MSC:

 11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure 11G30 Curves of arbitrary genus or genus $$\ne 1$$ over global fields 14H52 Elliptic curves

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### References:

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