Mahler measure
imported>Pythagoras0님의 2013년 6월 26일 (수) 08:04 판
introduction
- lehmer[x_] := 1 + x - x^3 - x^4 - x^5 - x^6 - x^7 + x^9 + x^10
p[x_] := x^4 - x^2 + 1
Plot[Log[Abs[p[Exp[2 Pi*I*t]]]], {t, 0, 1}]
Exp[NIntegrate[Log[Abs[p[Exp[2 Pi*I*t]]]], {t, 0, 1}]]
encyclopedia
- http://en.wikipedia.org/wiki/Mahler_measure
- http://mathworld.wolfram.com/LehmersMahlerMeasureProblem.html
- http://mathworld.wolfram.com/MahlerMeasure.html
expositions
- The many aspects of Mahler's measure, Banff workshop, 2003
- Matilde N. Laln Mahler measures as values of regulators 2006
- Mahler's measure, hyperbolic geometry and the dilogarithm
articles
- A dynamical interpretation of the global canonical height on an elliptic curve
- Mahler's Measure and the Dilogarithm (I)
- Mahler's Measure and the Dilogarithm (II)
- Authors: David W. Boyd, Fernando Rodriguez-Villegas, Nathan M. Dunfield
- http://maths.dur.ac.uk/~dma0hg/myres.html
- C. J. Smyth, An explicit formula for the Mahler measure of a family of 3-variable polynomials, J. Th. Nombres Bordeaux 14 (2002), 683{700
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