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.

引用

页码：5513 / 5516

页数：4

共 21 条

[1] ON THEOREMS OF WATSON AND DRAGONETTE FOR RAMANUJANS MOCK THETA FUNCTIONS [J].