Research in Number Theory

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A Gross–Kohnen–Zagier type theorem for higher-codimensional Heegner cycles

  • Shaul Zemel
Open Access


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.


Modular Form Cusp Form Automorphic Form Hodge Structure Abelian Surface 
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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Einstein Institute of Mathematicsthe Hebrew University of Jerusalem, Edmund Safra CampusJerusalemIsrael

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