"Smyth formula for Mahler measures"의 두 판 사이의 차이
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imported>Pythagoras0 (새 문서: ==introduction== ;thm '''[Smyth1981]''' $$ m(1+x_1+x_2)=L_{-3}'(-1)=\frac{3\sqrt{3}}{4\pi}L_{-3}(2)=0.3230659472\cdots \label{Smyth1} $$ $$ m(1+x_1+x_2+x_3)=14\zeta'(-2)=\frac{7}{2\p...) |
imported>Pythagoras0 |
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| 14번째 줄: | 14번째 줄: | ||
* using regulator | * using regulator | ||
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| + | ==expositions== | ||
| + | * Bertin, Marie-José, and MATILDE LALÍN. [http://www.dms.umontreal.ca/~mlalin/surveyMahlerfinal-revised.pdf Mahler Measure of Multivariable Polynomials] Women in Numbers 2: Research Directions in Number Theory 606 (2013): 125. | ||
| + | * Smyth, Chris. 2008. “The Mahler Measure of Algebraic Numbers: a Survey.” In Number Theory and Polynomials, 352:322–349. London Math. Soc. Lecture Note Ser. Cambridge: Cambridge Univ. Press. http://www.maths.ed.ac.uk/~chris/Smyth240707.pdf http://arxiv.org/pdf/math/0701397.pdf | ||
==articles== | ==articles== | ||
* '''[Smyth1981]''' Smyth, C. J. 1981. “On Measures of Polynomials in Several Variables.” Bulletin of the Australian Mathematical Society 23 (1): 49–63. doi:http://dx.doi.org/10.1017/S0004972700006894. | * '''[Smyth1981]''' Smyth, C. J. 1981. “On Measures of Polynomials in Several Variables.” Bulletin of the Australian Mathematical Society 23 (1): 49–63. doi:http://dx.doi.org/10.1017/S0004972700006894. | ||
2015년 1월 25일 (일) 00:20 판
introduction
- thm [Smyth1981]
$$ m(1+x_1+x_2)=L_{-3}'(-1)=\frac{3\sqrt{3}}{4\pi}L_{-3}(2)=0.3230659472\cdots \label{Smyth1} $$
$$ m(1+x_1+x_2+x_3)=14\zeta'(-2)=\frac{7}{2\pi^2}\zeta(3)=0.4262783988\cdots $$
two proofs of \ref{Smyth1}
- direct calculation
- using regulator
expositions
- Bertin, Marie-José, and MATILDE LALÍN. Mahler Measure of Multivariable Polynomials Women in Numbers 2: Research Directions in Number Theory 606 (2013): 125.
- Smyth, Chris. 2008. “The Mahler Measure of Algebraic Numbers: a Survey.” In Number Theory and Polynomials, 352:322–349. London Math. Soc. Lecture Note Ser. Cambridge: Cambridge Univ. Press. http://www.maths.ed.ac.uk/~chris/Smyth240707.pdf http://arxiv.org/pdf/math/0701397.pdf
articles
- [Smyth1981] Smyth, C. J. 1981. “On Measures of Polynomials in Several Variables.” Bulletin of the Australian Mathematical Society 23 (1): 49–63. doi:http://dx.doi.org/10.1017/S0004972700006894.