"Siegel-Weil formula"의 두 판 사이의 차이
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imported>Pythagoras0 (새 문서: ==introduction== * 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 e...) |
imported>Pythagoras0 |
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* It identifies the global theta lift of the trivial representation of $H(V_r)$ to $G(W_n)$ as an Eisenstein series | * 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. | * 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 | + | * Kudla and Rallis pushed the results to non-convergent regions [KR1-3] |
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==related items== | ==related items== | ||
* [[Classical theta lift and Shimura correspondence]] | * [[Classical theta lift and Shimura correspondence]] | ||
2014년 7월 11일 (금) 21:53 판
introduction
- 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]