Open Access System for Information Sharing

Login Library

 

Article
Cited 5 time in webofscience Cited 5 time in scopus
Metadata Downloads

On harmonic weak Maass forms of half integral weight SCIE SCOPUS

Title
On harmonic weak Maass forms of half integral weight
Authors
Bumkyu ChoChoie, Y
Date Issued
2013-08
Publisher
American Mathematical Society
Abstract
Since Zwegers found a connection between mock theta functions and harmonic weak Maass forms, this subject has been of vast research interest. In this paper, we obtain isomorphisms among the space H-k+1/2(+) (Gamma(0)(4m)) of (scalar valued) harmonic weak Maass forms of half integral weight whose Fourier coefficients are supported on suitable progressions, the space H-k+1/2x1,H- (rho) over barL of vector valued ones, and the space x1 (J) over cap (cusp)(k+1,m) of certain harmonic Maass-Jacobi forms of integral weight: H-k+1/2(+) (Gamma(0)(4m)) similar or equal to H-k+1/2,H-(rho) over barL similar or equal to (J) over cap (cusp)(k+1,m) for k odd and m = 1 or a prime. This is an extension of a result developed by Eichler and Zagier, which shows that M-k+1/2(+) (Gamma(0)(4m)) similar or equal to M-k+1/2,M-(rho) over barL similar or equal to J(k+1,m). Here M-k+1/2(+) (Gamma(0)(4m)), M-k+1/2,M-(rho) over barL and J(k+1,m) are the Kohnen plus space of (scalar valued) modular forms of half integral weight, the space of vector valued ones, and the space of Jacobi forms of integral weight, respectively. To extend the result, another approach is necessary because the argument by Eichler and Zagier depends on the dimension formulas for the spaces of holomorphic modular forms, but the dimensions for the spaces of harmonic weak Maass forms are not finite. Our proof relies on some nontrivial properties of the Weil representation.
URI
https://oasis.postech.ac.kr/handle/2014.oak/12717
DOI
10.1090/S0002-9939-2013-11549-2
ISSN
0002-9939
Article Type
Article
Citation
Proceedings of American Mathematical Society, vol. 141, no. 8, page. 2641 - 2652, 2013-08
Files in This Item:

qr_code

  • mendeley

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Related Researcher

Researcher

최영주CHOIE, YOUNG JU
Dept of Mathematics
Read more

Views & Downloads

Browse