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

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

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

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00209-017-2007-8

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title = "Shimura lifts of weakly holomorphic modular forms",

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{\textquoteright} 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.",

author = "Yingkun Li and Shaul Zemel",

note = "Publisher Copyright: {\textcopyright} 2017, Springer-Verlag GmbH Germany, part of Springer Nature.",

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AU - Zemel, Shaul

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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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U2 - 10.1007/s00209-017-2007-8

DO - 10.1007/s00209-017-2007-8

M3 - مقالة

SN - 0025-5874

VL - 290

SP - 37

EP - 61

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 1-2

ER -

Shimura lifts of weakly holomorphic modular forms

Abstract

All Science Journal Classification (ASJC) codes

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