Shimura lifts of weakly holomorphic modular forms

Yingkun Li; Shaul Zemel

doi:10.1007/s00209-017-2007-8

Shimura lifts of weakly holomorphic modular forms

Yingkun Li^*
, Shaul Zemel

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We show how to realize the Shimura lift of arbitrary level and character using the vector-valued theta lifts of Borcherds. Using the regularization of Borcherds’ lift we extend the Shimura lift to take weakly holomorphic modular forms of half-integral weight to meromorphic modular forms of even integral weight having poles at CM points.

Original language	English
Pages (from-to)	37-61
Number of pages	25
Journal	Mathematische Zeitschrift
Volume	290
Issue number	1-2
DOIs	https://doi.org/10.1007/s00209-017-2007-8
State	Published - 1 Oct 2018

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© 2017, Springer-Verlag GmbH Germany, part of Springer Nature.

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AB - We show how to realize the Shimura lift of arbitrary level and character using the vector-valued theta lifts of Borcherds. Using the regularization of Borcherds’ lift we extend the Shimura lift to take weakly holomorphic modular forms of half-integral weight to meromorphic modular forms of even integral weight having poles at CM points.

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Shimura lifts of weakly holomorphic modular forms

Abstract

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