The Mahler measure of x+1/x+y+1/y+4±42 and Beilinson's conjecture.

In this note we study the Mahler measures of reciprocal polynomials P k = x + 1 / x + y + 1 / y + k for k = 4 ± 4 2 . We prove identities relating the Mahler measure of P 4 ± 4 2 to special values of the L -functions of weight 2 cusp forms of level 64. We also express the Beilinson regulator which is a 2 × 2 determinant of Mahler measures as special value of L -function of the elliptic curve defined by P 4 + 4 2 = 0. [ABSTRACT FROM AUTHOR]