Mahler measure
imported>Pythagoras0님의 2012년 11월 3일 (토) 03:03 판 (찾아 바꾸기 – “* 논문정 리” 문자열을 “” 문자열로)
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}]]
history
encyclopedia
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Mahler_measure
- http://mathworld.wolfram.com/LehmersMahlerMeasureProblem.html
- http://mathworld.wolfram.com/MahlerMeasure.html
- http://en.wikipedia.org/wiki/
books
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
expositions
- 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
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- http://dx.doi.org/
question and answers(Math Overflow)
blogs
experts on the field