Abstract
We prove that the Heegner cycles of codimension m+1 inside Kuga-Sato type varieties of dimension 2m+1 are coefficients of modular forms of weight 3/2+m in the appropriate quotient group. The main technical tool for generating the necessary relations is a Borcherds style theta lift with polynomials. We also show how this lift defines a new singular Shimura-type correspondence from weakly holomorphic modular forms of weight 1/2−m to meromorphic modular forms of weight 2m+2.
Original language | American English |
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Article number | 23 |
Journal | Research in Number Theory |
Volume | 1 |
Issue number | 1 |
DOIs | |
State | Published - 1 Dec 2015 |
Bibliographical note
Funding Information:Authors’ information: The initial stage of this research has been carried out as part of my Ph.D. thesis work at the Hebrew University of Jerusalem, Israel. The final stage of this work was carried out at the Technical University of Darmstadt, Germany and supported by the Minerva Fellowship (Max-Planck-Gesellschaft).
Publisher Copyright:
© 2015, The Author(s).