New Theta-Function Identities of Level 6 in the Spirit of Ramanujan

被引：1

作者：

Srivatsa Kumar, B. R. ^{[1
]}

Rajanna, K. R. ^{[2
]}

Narendra, R. ^{[2
]}

机构：

[1] Manipal Acad Higher Educ, Manipal Inst Technol, Dept Math, Manipal 576104, Karnataka, India

[2] Acharya Inst Technol, Dept Math, Bangalore 560107, Karnataka, India

来源：

MATHEMATICAL NOTES | 2019年 / 106卷 / 5-6期

关键词：

theta-functions; Dedekind eta-function; modular equations; colored partitions; MODULAR EQUATIONS;

D O I：

10.1134/S0001434619110282

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Michael Somos discovered several theta-function identities of various levels by computer and offered no proof for them. These identities highly resemble some of Ramanujan's identities. The main focus of this paper is to prove some of these theta-function identities, in particular those of level 6 that have been discovered using computational searches. Some of the the Somos identities that we are discussing in this paper cannot be expressed in the form of P --Q type. Furthermore, we establish certain colored partition identities for them.

引用

页码：922 / 929

页数：8

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