Siegel-Weil formula
imported>Pythagoras0님의 2014년 7월 11일 (금) 22:39 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]
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.