ASYMPTOTICS FOR RANK PARTITION FUNCTIONS

被引：28

作者：

Bringmann, Kathrin ^{[1
]}

机构：

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

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 361卷 / 07期

关键词：

MOCK THETA-FUNCTIONS;

D O I：

10.1090/S0002-9947-09-04553-X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we obtain asymptotic formulas for an in finite class of rank generating functions. As an application, we solve a conjecture of Andrews and Lewis on inequalities between certain ranks.

引用

页码：3483 / 3500

页数：18

共 14 条

[1]

Andrews G.E., 1998, THEORY PARTITIONS

[2]

Andrews G.E., 1989, Theta functions-Bowdoin 1987, V49, P283

[3] The ranks and cranks of partitions moduli 2, 3, and 4 [J].

Andrews, GA ;

Lewis, R .

JOURNAL OF NUMBER THEORY, 2000, 85 (01) :74-84

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

ANDREWS, GE .

AMERICAN JOURNAL OF MATHEMATICS, 1966, 88 (02) :454-&

[5]

Atkin A.O.L., 1954, Proc. London Math. Soc. 3, V4, P84, DOI DOI 10.1112/PLMS/S3-4.1.84

[6]

BRINGMANN K, ANN 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] SOME ASYMPTOTIC FORMULAE FOR THE MOCK THETA-SERIES OF RAMANUJAN [J].

DRAGONETTE, LA .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1952, 72 (MAY) :474-500

[9]

Du D., 1944, EUREKA CAMBRIDGE, V8, P10

[10]

Dyson FJ., 1988, RAMANUJAN REVISITED, P7

← 1 2 →