منابع مشابه
Mahler Measure and the Wz Algorithm
We use the Wilf-Zeilberger method to prove identities between Mahler measures of polynomials. In particular, we offer a new proof of a formula due to Laĺın, and we show how to translate the identity into a formula involving elliptic dilogarithms. This work settles a challenge problem proposed by Kontsevich and Zagier in their paper “Periods” [14].
متن کاملOn the Mahler Measure Of
We prove a conjectured formula relating the Mahler measure of the Laurent polynomial 1 + X + X−1 + Y + Y −1, to the L-series of a conductor 15 elliptic curve.
متن کاملMahler ’ S Measure and the Dilogarithm
We continue to investigate the relation between the Mahler measure of certain two variable polynomials, the values of the Bloch–Wigner dilogarithm D(z) and the values ζF (2) of zeta functions of number fields. Specifically, we define a class A of polynomials A with the property that πm(A) is a linear combination of values D at algebraic arguments. For many polynomials in this class the correspo...
متن کاملMahler ’ S Measure and the Dilogarithm ( Ii
We continue to investigate the relation between the Mahler measure of certain two variable polynomials, the values of the Bloch–Wigner dilogarithm D(z) and the values ζF (2) of zeta functions of number fields. Specifically, we define a class A of polynomials A with the property that πm(A) is a linear combination of values D at algebraic arguments. For many polynomials in this class the correspo...
متن کاملPolynomials with small Mahler measure
We describe several searches for polynomials with integer coefficients and small Mahler measure. We describe the algorithm used to test Mahler measures. We determine all polynomials with degree at most 24 and Mahler measure less than 1.3, test all reciprocal and antireciprocal polynomials with height 1 and degree at most 40, and check certain sparse polynomials with height 1 and degree as large...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2015
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2015-12240-x