Shimura lifting on weak Maass forms

Youngju Choie, and Subong Lim. "Shimura lifting on weak Maass forms." Acta Arithmetica 173.1 (2016): 1-18. <http://eudml.org/doc/279789>.

@article{YoungjuChoie2016,
abstract = {There is a Shimura lifting which sends cusp forms of a half-integral weight to holomorphic modular forms of an even integral weight. Niwa and Cipra studied this lifting using the theta series attached to an indefinite quadratic form; later, Borcherds and Bruinier extended this lifting to weakly holomorphic modular forms and harmonic weak Maass forms of weight 1/2, respectively. We apply Niwa's theta kernel to weak Maass forms by using a regularized integral. We show that the lifted function satisfies modular transformation properties and is an eigenfunction of the Laplace operator. In particular, this lifting preserves the property of being harmonic. Furthermore, we determine the location of singularities of the lifted function and describe its singularity type.},
author = {Youngju Choie, Subong Lim},
journal = {Acta Arithmetica},
keywords = {Shimura lifting; weak Maass forms; regularized integral},
language = {eng},
number = {1},
pages = {1-18},
title = {Shimura lifting on weak Maass forms},
url = {http://eudml.org/doc/279789},
volume = {173},
year = {2016},
}

TY - JOUR
AU - Youngju Choie
AU - Subong Lim
TI - Shimura lifting on weak Maass forms
JO - Acta Arithmetica
PY - 2016
VL - 173
IS - 1
SP - 1
EP - 18
AB - There is a Shimura lifting which sends cusp forms of a half-integral weight to holomorphic modular forms of an even integral weight. Niwa and Cipra studied this lifting using the theta series attached to an indefinite quadratic form; later, Borcherds and Bruinier extended this lifting to weakly holomorphic modular forms and harmonic weak Maass forms of weight 1/2, respectively. We apply Niwa's theta kernel to weak Maass forms by using a regularized integral. We show that the lifted function satisfies modular transformation properties and is an eigenfunction of the Laplace operator. In particular, this lifting preserves the property of being harmonic. Furthermore, we determine the location of singularities of the lifted function and describe its singularity type.
LA - eng
KW - Shimura lifting; weak Maass forms; regularized integral
UR - http://eudml.org/doc/279789
ER -