Shimura lifting on weak Maass forms

• Autorzy: Youngju Choie , Subong Lim
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11F27: Theta series; Weil representation; theta correspondences

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 173
• Numer: 1
• Strony: 1-18

Daty

wydano

2016

Twórcy

autor

Youngju Choie

• Department of Mathematics and PMI, Pohang University of Science and Technology, Pohang, 790-784, Republic of Korea

autor

Subong Lim

• Department of Mathematics Education, Sungkyunkwan University, 25-2, Sungkyunkwan-ro, Jongno-gu, Seoul, 03063, Republic of Korea

Identyfikatory

DOI

10.4064/aa7916-12-2015