MOCK MAASS THETA FUNCTIONS

被引：9
作者：
Zwegers, Sander P. [1 ]
机构：
[1] Univ Cologne, Math Inst, D-50931 Cologne, Germany
来源：
QUARTERLY JOURNAL OF MATHEMATICS | 2012年 / 63卷 / 03期
关键词：
REAL QUADRATIC FIELDS; SERIES;
D O I：
10.1093/qmath/har020
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The purpose of this paper is to use a general class of indefinite theta functions to explain and generalize an example of a Maass waveform that was constructed by Cohen from two functions sigma and sigma*, studied by Andrews, Dyson and Hickerson. For this, we construct certain functions attached to an indefinite binary quadratic form and show that they are 'nearly' Maass waveforms. We call these functions mock Maass theta functions. In certain special cases we obtain actual Maass waveforms. These are the same as in the work of Maass.
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收藏
页码：753 / 770
页数：18
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