On the Mahler Measure of 1+X+1/X+Y +1/Y

By Mathew Rogers, Wadim Zudilin. 2011

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.The study of multi-variable Mahler measures originated in the work of Smyth, whoproved relations with Dirichlet L-values and special values of the Riemann zetafunction [22]. Formula (1) is the first known relation between a Mahler measureand the L-series of an elliptic curve. The original formulation is due to Deninger,who proved that the identity follows, up to an unknown rational factor, from theBeilinson conjectures [9]. Boyd subsequently calculated the rational factors, andalso found [5] that similar identities were numerically true for the polynomial familyk + X + X

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

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