ON THE TENTH-ORDER MOCK THETA FUNCTIONS

被引：5
作者：
Mortenson, Eric T. [1 ]
机构：
[1] Max Planck Inst Math, Vivatsgasse 7, D-53111 Bonn, Germany
来源：
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2018年 / 104卷 / 01期
关键词：
mock theta functions; Appell-Lerch functions; RAMANUJANS LOST NOTEBOOK; APPELL-LERCH SUMS; DYSONS RANKS; FORMS;
D O I：
10.1017/S1446788717000015
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Using properties of Appell-Lerch functions, we give insightful proofs for six of Ramanujan's identities for the tenth-order mock theta functions.
引用
收藏
页码：44 / 62
页数：19
相关论文
共 18 条
[1]   RAMANUJAN LOST NOTEBOOK .7. THE 6TH ORDER MOCK THETA FUNCTIONS [J].
ANDREWS, GE ;
HICKERSON, D .
ADVANCES IN MATHEMATICS, 1991, 89 (01) :60-105
[2]   THE 5TH AND 7TH ORDER MOCK THETA-FUNCTIONS [J].
ANDREWS, GE .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 293 (01) :113-134
[3]  
Bringmann K, 2008, J AM MATH SOC, V21, P1085
[4]   Dyson's ranks and Maass forms [J].
Bringmann, Kathrin ;
Ono, Ken .
ANNALS OF MATHEMATICS, 2010, 171 (01) :419-449
[5]   Tenth order mock theta functions in Ramanujan's lost notebook III [J].
Choi, Youn-Seo .
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2007, 94 :26-52
[6]   Tenth order mock theta functions in Ramanujan's lost notebook [J].
Choi, YS .
INVENTIONES MATHEMATICAE, 1999, 136 (03) :497-569
[7]   Tenth order mock theta functions in Ramanujan's lost notebook II [J].
Choi, YS .
ADVANCES IN MATHEMATICS, 2000, 156 (02) :180-285
[8]   A PROOF OF THE MOCK THETA-CONJECTURES [J].
HICKERSON, D .
INVENTIONES MATHEMATICAE, 1988, 94 (03) :639-660
[9]   Dyson's ranks and Appell-Lerch sums [J].
Hickerson, Dean ;
Mortenson, Eric .
MATHEMATISCHE ANNALEN, 2017, 367 (1-2) :373-395
[10]   Heeke-type double sums, Appell Lerch sums, and mock theta functions, I [J].
Hickerson, Dean R. ;
Mortenson, Eric T. .
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2014, 109 :382-422
12