Mahler measures and computations with regulators

Abstract

In this work we apply the techniques that were developed in [Lalin: An algebraic integration for Mahler measure] in order to study several examples of multivariable polynomials whose Mahler measure is expressed in terms of special values of the Riemann zeta function or Dirichlet L-series. The examples may be understood in terms of evaluations of regulators. Moreover, we apply the same techniques to the computation of generalized Mahler measures, in the sense of Gon and Oyanagi [Gon, Oyanagi: Generalized Mahler measures and multiple sine functions]

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References in corpus (5)

• Some examples of Mahler measures as multiple polylogarithms
• An algebraic integration for Mahler measure
• Explicit regulator maps on polylogarithmic motivic complexes
• On certain combination of colored multizeta values
• Goncharov's relations in Bloch's higher Chow group CH^3(F,5)

Cited by in corpus (7)

• Mahler measures and Fuglede--Kadison determinants
• An algebraic integration for Mahler measure
• A generalization of a theorem of Boyd and Lawton
• Heights of hypersurfaces in toric varieties
• Mahler measures of elliptic modular surfaces
• A Proof of the Conjecture of Lehmer and of the Conjecture of Schinzel-Zassenhaus
• An invariant property of Mahler measure