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

Shaul Zemel*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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 languageAmerican English
Article number23
JournalResearch in Number Theory
Volume1
Issue number1
DOIs
StatePublished - 1 Dec 2015

Bibliographical note

Publisher Copyright:
© 2015, The Author(s).

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