MODULAR TRANSFORMATIONS INVOLVING THE MORDELL INTEGRAL IN RAMANUJAN'S LOST NOTEBOOK

被引：0
作者：
Choi, Youn-Seo [1 ]
机构：
[1] Korea Inst Adv Study, Sch Math, Seoul 130722, South Korea
来源：
PACIFIC JOURNAL OF MATHEMATICS | 2014年 / 272卷 / 01期
基金：
新加坡国家研究基金会;
关键词：
Mordell integral; Appell-Lerch sum; Ramanujan;
D O I：
10.2140/pjm.2014.272.59
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In his "lost notebook" (p. 202 of the 1988 edition), S. Ramanujan recorded modular transformations involving the Mordell integral, q-hypergeometric series, and generalized Lambert series. He gave no proofs; here we prove these formulas and use them to derive modular transformations of third-order mock theta functions. Mordell's formula, the properties of q-hypergeometric series and Appell-Lerch sums play central roles in the proofs.
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收藏
页码：59 / 85
页数：27
相关论文
共 13 条
[1]   RAMANUJAN LOST NOTEBOOK .4. THE MOCK-THETA-CONJECTURES [J].
ANDREWS, GE ;
GARVAN, FG .
ADVANCES IN MATHEMATICS, 1989, 73 (02) :242-255
[2]  
Andrews GE., 1981, Mordell Integrals and Ramanujans Lost. Lecture Notes in Mathematics, P10
[3]   The basic bilateral hypergeometric series and the mock theta functions [J].
Choi, Youn-Seo .
RAMANUJAN JOURNAL, 2011, 24 (03) :345-386
[4]   Tenth order mock theta functions in Ramanujan's lost notebook (IV) [J].
Choi, YS .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 354 (02) :705-733
[5]   Generalization of two identities in Ramanujan's lost notebook [J].
Choi, YS .
ACTA ARITHMETICA, 2004, 114 (04) :369-389
[6]  
Kronecker L., 1889, ANGEW MATH, V105, P267
[7]  
KRONECKER L, 1889, J REINE ANGEW MATH, V105, P345
[8]   The definite integral integral(infinity)(-infinity)e(ax2)+bx/e(cx)+ddx and the analytic theory of numbers. [J].
Mordell, LJ .
ACTA MATHEMATICA, 1933, 61 (01) :323-360
[9]  
MORDELL LJ, 1920, Q J MATH, V48, P329
[10]  
Ramanujan S., 1988, LOST NOTEBOOK OTHER
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