A functional identity for Mahler measures of non-tempered polynomials. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Samart, Detchat
• Is Part Of: Integral transforms and special functions. Volume 32:Issue 1(2021)
• Page Start: 78
• Page End: 89
• Publication Date: 2021-01-02
• Subjects: Mahler measure -- elliptic integrals -- L-functions -- elliptic curves; 11R06 -- 11F67 -- 11G05 -- 33C75 -- 33E05; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2020.1799357
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: We establish a functional identity for Mahler measures of the two-parametric family P a, c ( x, y ) = a ( x + 1 / x ) + y + 1 / y + c . Our result extends an identity proven in a paper of Lalín, Zudilin and Samart. As a by-product, we obtain evaluations of m ( P a, c ) for some algebraic values of a and c in terms of special values of L -functions and logarithms. We also give a sufficient condition for validity of a certain identity between the elliptic integrals of the first and the third kind, which implies several identities for m ( P a, c ) .