Log-Sine Evaluations of Mahler Measures, II
نویسندگان
چکیده
منابع مشابه
Log-sine Evaluations of Mahler Measures, Ii
We continue our analysis of higher and multiple Mahler measures using log-sine integrals as started in [7, 8]. This motivates a detailed study of various multiple polylogarithms [4] and worked examples are given. Our techniques enable the reduction of several multiple Mahler measures, and supply an easy proof of two conjectures by Boyd.
متن کاملLog-sine evaluations of Mahler measures
We provide evaluations of several recently studied higher and multiple Mahler measures using log-sine integrals. This is complemented with an analysis of generating functions and identities for log-sine integrals which allows the evaluations to be expressed in terms of zeta values or more general polylogarithmic terms. The machinery developed is then applied to evaluation of further families of...
متن کاملA 5 INTEGERS 12 A ( 2012 ) : John Selfridge Memorial Issue LOG - SINE EVALUATIONS OF MAHLER MEASURES , II
We continue the analysis of higher and multiple Mahler measures using log-sine integrals as started in “Log-sine evaluations of Mahler measures” and “Special values of generalized log-sine integrals” by two of the authors. This motivates a detailed study of various multiple polylogarithms and worked examples are given. Our techniques enable the reduction of several multiple Mahler measures, and...
متن کاملMahler measures, short walks and log-sine integrals
The Mahler measure of a polynomial in several variables has been a subject of much study over the past thirty years — very few closed forms are proven but more are conjectured. In the case of multiple Mahler measures more tractable but interesting families exist. Using values of log-sine integrals we provide systematic evaluations of various higher and multiple Mahler measures. The evaluations ...
متن کاملMinimal Mahler Measures
We determine the minimal Mahler measure of a primitive, irreducible, noncyclotomic polynomial with integer coefficients and fixed degree D, for each even degree D ≤ 54. We also compute all primitive, irreducible, noncyclotomic polynomials with measure less than 1.3 and degree at most 44.
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ژورنال
عنوان ژورنال: Integers
سال: 2012
ISSN: 1867-0652,1867-0652
DOI: 10.1515/integers-2012-0035