"Mahler measure"의 두 판 사이의 차이
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imported>Pythagoras0 |
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==introduction== | ==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}]] | ||
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==related items== | ==related items== | ||
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==encyclopedia== | ==encyclopedia== | ||
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* http://mathworld.wolfram.com/MahlerMeasure.html | * http://mathworld.wolfram.com/MahlerMeasure.html | ||
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* [http://www.math.ca/notes/v34/n2/Notesv34n2.pdf Mahler's measure, hyperbolic geometry and the dilogarithm] | * [http://www.math.ca/notes/v34/n2/Notesv34n2.pdf Mahler's measure, hyperbolic geometry and the dilogarithm] | ||
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==articles== | ==articles== | ||
| − | + | * Zudilin, Wadim. 2013. “Regulator of Modular Units and Mahler Measures”. ArXiv e-print 1304.3869. http://arxiv.org/abs/1304.3869. | |
| − | * | + | * A dynamical interpretation of the global canonical height on an elliptic curve |
| − | * [http://www.smc.math.ca/cjm/v54/p468 Mahler's Measure and the Dilogarithm (I)] | + | * [http://www.smc.math.ca/cjm/v54/p468 Mahler's Measure and the Dilogarithm (I)] |
| − | + | * [http://arxiv.org/abs/math.NT/0308041 Mahler's Measure and the Dilogarithm (II)] | |
| − | * [http://arxiv.org/abs/math.NT/0308041 Mahler's Measure and the Dilogarithm (II)] | ||
** Authors: David W. Boyd, Fernando Rodriguez-Villegas, Nathan M. Dunfield | ** Authors: David W. Boyd, Fernando Rodriguez-Villegas, Nathan M. Dunfield | ||
* [http://maths.dur.ac.uk/%7Edma0hg/myres.html http://maths.dur.ac.uk/~dma0hg/myres.html] | * [http://maths.dur.ac.uk/%7Edma0hg/myres.html http://maths.dur.ac.uk/~dma0hg/myres.html] | ||
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==blogs== | ==blogs== | ||
| − | * http://enyokoyama.blogspot.com/2012/05/mahlers-measure-hyperbolic-geometry-and.html | + | * http://enyokoyama.blogspot.com/2012/05/mahlers-measure-hyperbolic-geometry-and.html 구글 블로그 검색 |
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[[분류:개인노트]] | [[분류:개인노트]] | ||
[[Category:research topics]] | [[Category:research topics]] | ||
2013년 6월 28일 (금) 11:23 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
- Zudilin, Wadim. 2013. “Regulator of Modular Units and Mahler Measures”. ArXiv e-print 1304.3869. http://arxiv.org/abs/1304.3869.
- 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