Mahler measures and modular funs

Abstract

In my talk I will report on my recent work with Mat Rogers towards Boyd's conjectural evaluations of Mahler measures of 2-variate polynomials. Although the grounds for these conjectures come from K-theory, our technique is completely analytical and even elementary. One of the crucial ingredients of our proofs is numerous identities between the signature 3 theta functions, the subject developed in many works of Jonathan Borwein and his collaborators.

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