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
Andrews, GA
Lewis, R
[J]. JOURNAL OF NUMBER THEORY, 2000, 85 (01) : 74 - 84
[4] ON THEOREMS OF WATSON AND DRAGONETTE FOR RAMANUJANS MOCK THETA FUNCTIONS
ANDREWS, GE
[J]. 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
Bringmann, Kathrin
Ono, Ken
[J]. INVENTIONES MATHEMATICAE, 2006, 165 (02) : 243 - 266
[8] SOME ASYMPTOTIC FORMULAE FOR THE MOCK THETA-SERIES OF RAMANUJAN
DRAGONETTE, LA
[J]. 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 →