John D. Condon
Published 2011-11-01, updated 2011-11-11Version 2
We show that for almost every polynomial P(x,y) with complex coefficients, the difference of the logarithmic Mahler measures of P(x,y) and P(x,x^n) can be expanded in a type of formal series similar to an asymptotic power series expansion in powers of 1/n. This generalizes a result of Boyd. We also show that such an expansion is unique and provide a formula for its coefficients. When P has algebraic coefficients, the coefficients in the expansion are linear combinations of polylogarithms of algebraic numbers, with algebraic coefficients.
Comments: 25 pages. V2: Demoted previous Corollary 1 to a comment, after realizing that Boyd had already proved that bit. Made small corrections to Lemma 5, streamlined the proof of Lemma 9, and reworded section 9.3
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Difference of a Hauptmodul for $Γ_{0}(N)$
Relations for the difference of two dilogarithms
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