Spectacle cycles with coefficients and modular forms of half-integral weight

Funke, J.; Millson, J.

Abstract

In this paper we present a geometric way to extend the Shintani lift from even weight cusp forms for congruence subgroups to arbitrary modular forms, in particular Eisenstein series. This is part of our eorts to extend in the noncompact situation the results of Kudla-Millson and Funke-Millson relating Fourier coecients of (Siegel) modular forms with intersection numbers of cycles (with coe cients) on orthogonal locally symmetric spaces. In the present paper, the cycles in question are the classical modular symbols with nontrivial coecients. We introduce \capped" modular symbols with coecients which we call \spectacle cycles" and show that the generating series of cohomological periods of any modular form over the spectacle cycles is a modular form of half-integral weight.

Citation

Funke, J., & Millson, J. (2011). Spectacle cycles with coefficients and modular forms of half-integral weight. In J. Cogdell, J. Funke, M. Rapoport, & T. Yang (Eds.), Arithmetic geometry and automorphic forms (91-154). International Press

• Publication Date: Dec 31, 2011
• Deposit Date: Feb 28, 2011
• Publicly Available Date: May 14, 2014
• Publisher: International Press
• Pages: 91-154
• Series Title: Advanced lectures in mathematics.
• Book Title: Arithmetic geometry and automorphic forms.
• Publisher URL: http://intlpress.com/site/pub/pages/books/items/00000365/index.html
• Additional Information: Volume in honor of the 60th birthday of Stephen S. Kudla.