On modular relations for the Gollnitz-Gordon functions with applications to partitions

被引：30

作者：

Huang, SS ^{[1
]}

机构：

[1] Natl Chang Hua Univ Educ, Dept Math, Chang Hua, Taiwan

来源：

JOURNAL OF NUMBER THEORY | 1998年 / 68卷 / 02期

关键词：

Rogers-Ramanujan functions (identities); Gollnitz-Gordon functions (identities); Dedekind eta-functions; partitions; colored partitions;

D O I：

10.1006/jnth.1997.2205

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In a manuscript of Ramanujan. published with his Lost Notebook [21, pp. 236-337], there are forty identities involving the Rogers-Ramunujan functions. According to G. N. Watson, the beauty of these identities are comparable to that of the Rogers-Ramanujan identities. In the paper, we establish modular relations involving the Gollnitz-Gordon Functions which are analogous to Ramanujan's forty identities. Furthermore, ae extract interesting partition results from some of the modular relations. (C) 1998 Academic Press.

引用

页码：178 / 216

页数：39

共 23 条

[1]

Andrews G. E., 1976, The Theory of Partitions

[2]

BAXTER RJ, 1988, RAMANUJAN REVISITED, P69

[3]

Berndt B. C., 1991, Ramanujan's Notebooks

[4] A PROOF OF SOME IDENTITIES OF RAMANUJAN USING MODULAR-FORMS [J].

BIAGIOLI, AJF .

GLASGOW MATHEMATICAL JOURNAL, 1989, 31 :271-295

[5] LOOK BACK AT RAMANUJANS NOTEBOOKS [J].

BIRCH, BJ .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1975, 78 (JUL) :73-79

[6]

Bressoud D., 1977, Proof and Generalization of Certain Identities Conjectured by Ramanujan

[7]

BRESSOUD DM, 1977, J LOND MATH SOC, V16, P9

[8]

CHAN HH, 1997, RAMANUJAN J, V1, P75

[9]

Darling HBC, 1921, P LOND MATH SOC, V19, P350

[10]

Fine N. J., 1988, Amer. Math. Soc., V27

← 1 2 3 →