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ON A CONJECTURE BY BOYD

The aim of this note is to prove the Mahler measure identity m(x + x-1 + y + y-1 + 5) = 6m(x + x-1 + y + y-1 + 1) which was conjectured by Boyd. The proof is achieved by proving relationships between regulators of both curves.

Matilde N. Lalin | M. Lalín

[1] J. Cassels. Lectures on elliptic curves , 1991 .

[2] Matilde N. Lal'in,et al. Functional equations for Mahler measures of genus-one curves , 2006, math/0612007.

[3] M. Bertin. Mesure de Mahler d''une famille de polyn?omes , 2004 .

[4] M. A. Bennett,et al. Number Theory for the Millennium I , 2002 .

[5] W. Leveque. Topics in number theory , 1956 .

[6] Christopher Deninger,et al. Deligne periods of mixed motives, -theory and the entropy of certain ℤⁿ-actions , 1997 .

[7] N. Kurokawa,et al. Mahler Measures via the Crystalization , 2005 .

[8] Fernando Rodriguez-Villegas. Identities between Mahler measures , 2006 .

[9] J. Cassels. LMSST: 24 Lectures on Elliptic Curves , 1991 .

[10] David W. Boyd,et al. Mahler's Measure and Special Values of L-functions , 1998, Exp. Math..

[11] F. Rodriguez Villegas,et al. Modular Mahler Measures I , 1999 .