A 5 INTEGERS 12 A ( 2012 ) : John Selfridge Memorial Issue LOG - SINE EVALUATIONS OF MAHLER MEASURES , II
نویسندگان
چکیده
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 supply an easy proof of two conjectures by Boyd. –This paper is dedicated to the memory of John Selfridge
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 کامل# A 6 INTEGERS 12 A ( 2012 ) : John Selfridge Memorial Issue ON ODD PERFECT NUMBERS AND EVEN 3 - PERFECT NUMBERS
An idea used in the characterization of even perfect numbers is used, first, to derive new necessary conditions for the existence of an odd perfect number and, second, to show that there are no even 3-perfect numbers of the form 2aM , where M is odd and squarefree and a ≤ 718, besides the six known examples. –In memory of John Selfridge
متن کامل#A16 INTEGERS 12A (2012): John Selfridge Memorial Issue THE SEARCH FOR AURIFEUILLIAN-LIKE FACTORIZATIONS
We searched the Cunningham tables for new algebraic factorizations similar to those discovered by Aurifeuille. A naive search would have been too slow. We accelerated it enough to make it feasible. Many interesting results were found. –Dedicated to the memory of John Selfridge, who loved the integers.
متن کامل#A3 INTEGERS 12A (2012): John Selfridge Memorial Issue PERFECT POWERS WITH FEW TERNARY DIGITS
We classify all integer squares (and, more generally, q-th powers for certain values of q) whose ternary expansions contain at most three digits. Our results follow from Padé approximants to the binomial function, considered 3-adically. –Dedicated to the memory of John Selfridge.
متن کامل#A15 INTEGERS 12A (2012): John Selfridge Memorial Issue EXPLICIT SOLUTIONS OF CERTAIN SYSTEMS OF PELL EQUATIONS
We show how to obtain the solutions of families of systems of two Pell equations; these families are parameterized by the prime numbers. -Dedicated to the memory of John Selfridge. His opera voice is no more, but his voice in mathematics will continue to be heard, powerful.
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تاریخ انتشار 2012