"Kohnen-Waldspurger formula"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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:<math>L(E(\Delta),1)=\alpha(\cdots)b_{E}(\Delta)^{2}</math><br> | :<math>L(E(\Delta),1)=\alpha(\cdots)b_{E}(\Delta)^{2}</math><br> | ||
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| + | ==related items== | ||
| + | * [[Gross-Zagier formula]] | ||
2013년 12월 30일 (월) 00:29 판
introduction
- In the 1980s, Waldspurger [205], and Kohnen and Zagier [135, 136, 137] established that certain half-integral weight modular forms serve as generating functions of a new type.
- Using the Shimura correspondence [192], they proved that certain coefficients of half-integral weight cusp forms essentially are square-roots of central values of quadratic twists of modular L-functions.
- There is a modular form $g(z)=\sum b_{E}(n)q^n$ such that if $\epsilon()=1$,
\[L(E(\Delta),1)=\alpha(\cdots)b_{E}(\Delta)^{2}\]
articles
- [135] W. Kohnen, Newforms of half-integral weight, J. Reine Angew. Math. 333 (1982) 32-72.
- [136] W. Kohnen, Fourier coefficients of modular forms of half-integral weight, Math. Ann. 271 (1985), 237-268. http://www.springerlink.com/content/p52527460724p36m/
- [137] W. Kohnen and D. Zagier, Values of L-series of modular forms at the center of the critical strip, Invent. Math. 64 (1981), no. 2, pages 175–198.
- [205] J.-L. Waldspurger, Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pures Appl. (9) 60 (1981), no. 4, pages 375–484.