A short proof of the Mock Theta Conjectures using Maass forms

被引:11
作者
Folsom, Amanda [1 ]
机构
[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA
关键词
D O I
10.1090/S0002-9939-08-09434-3
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A celebrated work of D. Hickerson gives a proof of the Mock Theta Conjectures using Hecke-type identities discovered by G. Andrews. Here, we respond to a remark by K. Bringmann, K. Ono and R. Rhoades and provide a short proof of the Mock Theta Conjectures by realizing each side of the identities as the holomorphic projection of a harmonic weak Maass form.
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页码:4143 / 4149
页数:7
相关论文
共 17 条
[1]   RAMANUJAN LOST NOTEBOOK .4. THE MOCK-THETA-CONJECTURES [J].
ANDREWS, GE ;
GARVAN, FG .
ADVANCES IN MATHEMATICS, 1989, 73 (02) :242-255
[2]   THE 5TH AND 7TH ORDER MOCK THETA-FUNCTIONS [J].
ANDREWS, GE .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 293 (01) :113-134
[3]  
Atkin A.O.L., 1954, Proc. Lond. Math. Soc., V4, P84, DOI DOI 10.1112/PLMS/S3-4.1.84
[4]  
BRINGMANN K, T AM MATH S IN PRESS
[5]  
BRINGMANN K, J AM MATH S IN PRESS
[6]  
BRINGMANN K, 2007, ANN MATH IN PRESS
[7]   The f(q) mock theta function conjecture and partition ranks [J].
Bringmann, Kathrin ;
Ono, Ken .
INVENTIONES MATHEMATICAE, 2006, 165 (02) :243-266
[8]   On two geometric theta lifts [J].
Bruinier, JH ;
Funke, J .
DUKE MATHEMATICAL JOURNAL, 2004, 125 (01) :45-90
[9]  
Dyson F.J., 1944, Eureka, V8, P10
[10]   A PROOF OF THE MOCK THETA-CONJECTURES [J].
HICKERSON, D .
INVENTIONES MATHEMATICAE, 1988, 94 (03) :639-660