On the Mahler measure of $1+X+1/X+Y+1/Y$

Abstract

We prove a conjectured formula relating the Mahler measure of the Laurent polynomial $1+X+X^{-1}+Y+Y^{-1}$, to the $L$-series of a conductor 15 elliptic curve.

18 pages, Fixed typos in Lemmas 3 and 4

References in corpus (4)

• From $L$-series of elliptic curves to Mahler measures
• Mahler's Measure and the Dilogarithm (II)
• On a conjecture by Boyd
• Mahler measure and the WZ algorithm

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• A functional identity for Mahler measures of non-tempered polynomials
• Transformations of $L$-values
• An invariant property of Mahler measure
• Mahler's measure and elliptic curves with potential complex multiplication
• Apéry's theorem and problems for the values of Riemann's zeta function and their $q$-analogues
• $L$-values for conductor $32$
• The Mahler measure of exact polynomials in three variables
• Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi