"Siegel-Weil formula"의 두 판 사이의 차이
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* Roughly speaking, the Siegel-Weil formula says that the theta integral associated to a vector space (quadratic or Hermitian) is the special value of some Eisenstein series at certain point when both the theta integral and Eisenstein series (at the point) are both absolutely convergent. | * Roughly speaking, the Siegel-Weil formula says that the theta integral associated to a vector space (quadratic or Hermitian) is the special value of some Eisenstein series at certain point when both the theta integral and Eisenstein series (at the point) are both absolutely convergent. | ||
* Kudla and Rallis pushed the results to non-convergent regions [KR1-3] | * Kudla and Rallis pushed the results to non-convergent regions [KR1-3] | ||
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| + | ==memo== | ||
| + | * [https://www.google.com.au/search?q=site:http:%2F%2Fwww.math.umn.edu%2F~garrett%2F+siegel&ei=_m07VdyHI8XvmAWpioDICw Google Paul Garret's webpage] | ||
2015년 4월 25일 (토) 03:35 판
introduction
- 틀:수학노트
- The Siegel-Weil formula was discovered by Siegel in the context of classical modular forms and then cast in the representation theoretic language and considerably extended in an influential paper of Weil
- It identifies the global theta lift of the trivial representation of $H(V_r)$ to $G(W_n)$ as an Eisenstein series
- Roughly speaking, the Siegel-Weil formula says that the theta integral associated to a vector space (quadratic or Hermitian) is the special value of some Eisenstein series at certain point when both the theta integral and Eisenstein series (at the point) are both absolutely convergent.
- Kudla and Rallis pushed the results to non-convergent regions [KR1-3]
memo
articles
- Gan, Wee Teck, and Shuichiro Takeda. 2009. “On the Regularized Siegel-Weil Formula (the Second Term Identity) and Non-Vanishing of Theta Lifts from Orthogonal Groups.” arXiv:0902.0419 [math], February. http://arxiv.org/abs/0902.0419.
- Kudla, Stephen S., and Stephen Rallis. 1994. “A Regularized Siegel-Weil Formula: The First Term Identity.” The Annals of Mathematics 140 (1): 1. doi:10.2307/2118540.