"라마누잔의 class invariants"의 두 판 사이의 차이
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| 1번째 줄: | 1번째 줄: | ||
| − | <h5> | + | <math>g_n:=(\frac{k'(i\sqrt{n})^2}{2k(i\sqrt{n})})^{1/12}</math> |
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| + | <math>g_{58}^2=\frac{\sqrt{29}+5}{2}</math> | ||
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| + | <h5>정의</h5> | ||
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| + | <math>q=e^{2\pi i \tau}</math> | ||
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| + | <math>\theta_{2}(\tau)= \sum_{n=-\infty}^\infty q^{(n+\frac{1}{2})^2/2}</math> | ||
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| + | <math>\theta_3(\tau)=\sum_{n=-\infty}^\infty q^{n^2/2}</math> | ||
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| + | <math>\theta_{4}(\tau)= \sum_{n=-\infty}^\infty (-1)^n q^{n^2/2}</math> | ||
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| + | <math>k=k(\tau)=\frac{\theta_2^2(\tau)}{\theta_3^2(\tau)}</math> | ||
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| 45번째 줄: | 67번째 줄: | ||
* [http://arxiv1.library.cornell.edu/abs/math/0308028v1 Ramanujan's Most Singular Modulus]<br> | * [http://arxiv1.library.cornell.edu/abs/math/0308028v1 Ramanujan's Most Singular Modulus]<br> | ||
| − | ** Mark B. Villarino | + | ** Mark B. Villarino, Arxiv, 2003-8 |
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* [http://matwbn.icm.edu.pl/ksiazki/aa/aa73/aa7316.pdf Ramanujan’s class invariants and cubic continued fraction]<br> | * [http://matwbn.icm.edu.pl/ksiazki/aa/aa73/aa7316.pdf Ramanujan’s class invariants and cubic continued fraction]<br> | ||
| − | ** BC Berndt, HH Chan, LC Zhang | + | ** BC Berndt, HH Chan, LC Zhang, ACTA ARITHMETICA LXXIII.1 (1995) |
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* [http://www.ams.org/tran/1997-349-06/S0002-9947-97-01738-8/S0002-9947-97-01738-8.pdf Ramanujan's class invariants, Kronecker's limit formula, and modular equations]<br> | * [http://www.ams.org/tran/1997-349-06/S0002-9947-97-01738-8/S0002-9947-97-01738-8.pdf Ramanujan's class invariants, Kronecker's limit formula, and modular equations]<br> | ||
| − | ** BC Berndt, HH Chan, LC Zhang | + | ** BC Berndt, HH Chan, LC Zhang, Transactions of the American Mathematical Society, 1997 |
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* [http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=20087 RAMANUJAN–WEBER CLASS INVARIANT Gn AND WATSON'S EMPIRICAL PROCESS]<br> | * [http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=20087 RAMANUJAN–WEBER CLASS INVARIANT Gn AND WATSON'S EMPIRICAL PROCESS]<br> | ||
| − | ** HH Chan | + | ** HH Chan, Journal of the London Mathematical Society, 1998 |
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* [http://www.journals.cms.math.ca/cgi-bin/vault/public/view/berndt7376/body/PDF/berndt7376.pdf Ramanujan and the modular j-invariant]<br> | * [http://www.journals.cms.math.ca/cgi-bin/vault/public/view/berndt7376/body/PDF/berndt7376.pdf Ramanujan and the modular j-invariant]<br> | ||
| − | ** BC Berndt, HH Chan | + | ** BC Berndt, HH Chan, Canadian Mathematical Bulletin, 1999 |
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* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
* http://en.wikipedia.org/wiki/ | * http://en.wikipedia.org/wiki/ | ||
2009년 8월 14일 (금) 10:09 판
\(g_n:=(\frac{k'(i\sqrt{n})^2}{2k(i\sqrt{n})})^{1/12}\)
\(g_{58}^2=\frac{\sqrt{29}+5}{2}\)
정의
\(q=e^{2\pi i \tau}\)
\(\theta_{2}(\tau)= \sum_{n=-\infty}^\infty q^{(n+\frac{1}{2})^2/2}\)
\(\theta_3(\tau)=\sum_{n=-\infty}^\infty q^{n^2/2}\)
\(\theta_{4}(\tau)= \sum_{n=-\infty}^\infty (-1)^n q^{n^2/2}\)
\(k=k(\tau)=\frac{\theta_2^2(\tau)}{\theta_3^2(\tau)}\)
하위주제들
재미있는 사실
관련된 다른 주제들
관련도서 및 추천도서
- Ramanujan's Notebooks: V
- Bruce C. Berndt
- 도서내검색
- 도서검색
참고할만한 자료
- Ramanujan's Most Singular Modulus
- Mark B. Villarino, Arxiv, 2003-8
- Ramanujan’s class invariants and cubic continued fraction
- BC Berndt, HH Chan, LC Zhang, ACTA ARITHMETICA LXXIII.1 (1995)
- Ramanujan's class invariants, Kronecker's limit formula, and modular equations
- BC Berndt, HH Chan, LC Zhang, Transactions of the American Mathematical Society, 1997
- RAMANUJAN–WEBER CLASS INVARIANT Gn AND WATSON'S EMPIRICAL PROCESS
- HH Chan, Journal of the London Mathematical Society, 1998
- Ramanujan and the modular j-invariant
- BC Berndt, HH Chan, Canadian Mathematical Bulletin, 1999
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- http://scholar.google.com/scholar?q=ramanujan%27s+class+invariants&hl=ko&lr=&start=10&sa=N
- 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=
- 다음백과사전 http://enc.daum.net/dic100/search.do?q=
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