"3rd order mock theta functions"의 두 판 사이의 차이
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+ | <h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">introduction</h5> | ||
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+ | * <math>f(q) = \sum_{n\ge 0} {q^{n^2}\over (-q;q)_n^2} = {2\over \prod_{n>0}(1-q^n)}\sum_{n\in Z}{(-1)^nq^{3n^2/2+n/2}\over 1+q^n}</math><br>[http://www.research.att.com/~njas/sequences/A000025 ]http://www.research.att.com/~njas/sequences/A000025<br>http://www.research.att.com/~njas/sequences/b000025.txt<br> | ||
+ | * good introduction is given in Andrews article <br> | ||
+ | ** [http://www.ingentaconnect.com/content/klu/rama/2003/00000007/F0030001/05142410 Partitions : at the interface of q-series and modular forms] | ||
+ | ** [http://www.ingentaconnect.com/content/klu/rama/2003/00000007/F0030001/05142410 ]section 5 | ||
+ | * the asymptotic series for coefficients of the order 3 mock theta function f(q) studied by of (Andrews 1966) and Dragonette (1952) converges to the coefficients ([http://www.springerlink.com/content/5524655155350464/ Bringmann & Ono 2006]). | ||
+ | * In particular Mock theta functions have asymptotic expansions at cusps of the modular group, acting on the upper half-plane, that resemble those of modular forms of weight 1/2 with poles at the cusps. | ||
+ | * [http://dx.doi.org/10.1112%2Fjlms%2Fs1-11.1.55 The Final Problem : An Account of the Mock Theta Functions]<br> | ||
+ | ** Watson, G. N. (1936), J. London Math. Soc. 11: 55–80 | ||
+ | * [http://dx.doi.org/10.2307%2F1990714 Some asymptotic formulae for the mock theta series of Ramanujan]<br> | ||
+ | ** Dragonette, Leila A. (1952), | ||
+ | ** Transactions of the American Mathematical Society 72: 474–500 | ||
+ | * [http://dx.doi.org/10.2307%2F2373202 On the theorems of Watson and Dragonette for Ramanujan's mock theta functions]<br> | ||
+ | ** Andrews, George E. (1966) | ||
+ | ** American Journal of Mathematics 88: 454–490 | ||
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+ | <h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">history</h5> | ||
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+ | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
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+ | <h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">related items</h5> | ||
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+ | <h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">encyclopedia</h5> | ||
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+ | * http://ko.wikipedia.org/wiki/ | ||
+ | * http://en.wikipedia.org/wiki/ | ||
+ | * Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]]) | ||
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+ | <h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">books</h5> | ||
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+ | * [[2010년 books and articles]]<br> | ||
+ | * http://gigapedia.info/1/ | ||
+ | * http://gigapedia.info/1/ | ||
+ | * http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords= | ||
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+ | [[4909919|]] | ||
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+ | * [[2010년 books and articles|논문정리]] | ||
+ | * 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://www.ams.org/mathscinet ] | ||
+ | * 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/ | ||
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+ | <h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">question and answers(Math Overflow)</h5> | ||
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+ | * http://mathoverflow.net/search?q= | ||
+ | * http://mathoverflow.net/search?q= | ||
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+ | <h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">blogs</h5> | ||
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+ | * 구글 블로그 검색<br> | ||
+ | ** http://blogsearch.google.com/blogsearch?q= | ||
+ | ** http://blogsearch.google.com/blogsearch?q= | ||
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+ | <h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">experts on the field</h5> | ||
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+ | * http://arxiv.org/ | ||
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+ | <h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">links</h5> | ||
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+ | * [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | ||
+ | * [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내] | ||
+ | * [http://www.research.att.com/~njas/sequences/index.html The On-Line Encyclopedia of Integer Sequences] | ||
+ | * http://functions.wolfram.com/ | ||
+ | * <br> |
2010년 7월 31일 (토) 13:56 판
introduction
- \(f(q) = \sum_{n\ge 0} {q^{n^2}\over (-q;q)_n^2} = {2\over \prod_{n>0}(1-q^n)}\sum_{n\in Z}{(-1)^nq^{3n^2/2+n/2}\over 1+q^n}\)
[1]http://www.research.att.com/~njas/sequences/A000025
http://www.research.att.com/~njas/sequences/b000025.txt - good introduction is given in Andrews article
- the asymptotic series for coefficients of the order 3 mock theta function f(q) studied by of (Andrews 1966) and Dragonette (1952) converges to the coefficients (Bringmann & Ono 2006).
- In particular Mock theta functions have asymptotic expansions at cusps of the modular group, acting on the upper half-plane, that resemble those of modular forms of weight 1/2 with poles at the cusps.
- The Final Problem : An Account of the Mock Theta Functions
- Watson, G. N. (1936), J. London Math. Soc. 11: 55–80
- Some asymptotic formulae for the mock theta series of Ramanujan
- Dragonette, Leila A. (1952),
- Transactions of the American Mathematical Society 72: 474–500
- On the theorems of Watson and Dragonette for Ramanujan's mock theta functions
- Andrews, George E. (1966)
- American Journal of Mathematics 88: 454–490
history
encyclopedia
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
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=
[[4909919|]]
articles
- 논문정리
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html[3]
- 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