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

Funke, J.; Millson, J.

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


Authors

J. Millson



Contributors

J. Cogdell
Editor

M. Rapoport
Editor

T. Yang
Editor

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 Mar 29, 2024
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.

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Copyright Statement
Copyright © International Press. First published in Arithmetic Geometry and Automorphic Forms in Advanced Lectures in Mathematics, Volume 19, 2011, published by International Press.




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