Rank and crank moments for overpartitions

被引：52

作者：

Bringmann, Kathrin ^{[1
]}

Lovejoy, Jeremy ^{[2
]}

Osburn, Robert ^{[3
]}

机构：

[1] Univ Cologne, Math Inst, D-50931 Cologne, Germany

[2] Univ Paris 07, CNRS, LIAFA, F-75251 Paris 05, France

[3] Univ Coll Dublin, Sch Math Sci, Dublin 4, Ireland

来源：

JOURNAL OF NUMBER THEORY | 2009年 / 129卷 / 07期

关键词：

FROBENIUS REPRESENTATION; PARTITIONS; CONJUGATION;

D O I：

10.1016/j.jnt.2008.10.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study two types of crank moments and two types of rank moments for overpartitions. We show that the crank moments and their derivatives, along with certain linear combinations of the rank moments and their derivatives, can be written in terms of quasimodular forms. We then use this fact to prove exact relations involving the moments as well as congruence properties modulo 3, 5, and 7 for some combinatorial functions which may be expressed in terms of the second moments. Finally, we establish a congruence modulo 3 involving one such combinatorial function and the Hurwitz class number H(n). (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：1758 / 1772

页数：15

共 21 条

[1] DYSONS CRANK OF A PARTITION [J].