Overpartitions and class numbers of binary quadratic forms

被引：29
|
作者：
Bringmann, Kathrin
Lovejoy, Jeremy
机构：
[1] Univ Cologne, Math Inst, D-50931 Cologne, Germany
[2] Univ Paris 07, Ctr Natl Rech Sci, Lab Informat Algorithm, F-75205 Paris 13, France
来源：
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | 2009年 / 106卷 / 14期
关键词：
congruences; harmonic Maass form; mock theta function; Dyson's rank; Zagier-Eisenstein series; MODULAR-FORMS; PARTITIONS;
D O I：
10.1073/pnas.0900783106
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
We show that the Zagier-Eisenstein series shares its nonholomorphic part with certain weak Maass forms whose holomorphic parts are generating functions for overpartition rank differences. This has a number of consequences, including exact formulas, asymptotics, and congruences for the rank differences as well as q-series identities of the mock theta type.
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页码：5513 / 5516
页数：4
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