A Proof of some identities of Ramanujan using modular forms

Author:

Biagioli Anthony J. F.

Abstract

In 1974 B. J. Birch [1] published a description of some manuscripts of Ramanujan which contained, among other things, a list of forty identities involving the Rogers-Ramanujan functionsAt that time nine of these had been proven, and since then twenty-two more of them have been proven, fifteen of them by David Bressoud in his thesis [2]. Bressoud gives a synopsis of the extant proofs, where he attributes proofs to H. B. C. Darling [3], L. J. Rogers [4], L. J. Mordell [5], and G. N. Watson [6].

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference13 articles.

1. Ramanujan's ”mixed” modular equations;Berndt;J. Ramanujan Math. Soc.,1986

2. 2. Bressoud David , Proof and generalization of certain identities conjectured by Ramanujan (thesis, Temple university 1980).

3. Elliptic Modular Functions

Cited by 42 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The deviation on cranks of partitions;Journal of Symbolic Computation;2025-01

2. Deviation of the rank and crank modulo 11;The Ramanujan Journal;2024-05-21

3. New symmetries for Dyson’s rank function;The Ramanujan Journal;2024-04-03

4. A modular approach to Andrews-Beck partition statistics;Journal of Combinatorial Theory, Series A;2024-04

5. On Ramanujan's lost notebook and new tenth‐order like identities for second‐, sixth‐, and eighth‐order mock theta functions;Bulletin of the London Mathematical Society;2023-12-26

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3