Generalizations of Ramanujan's reciprocity theorem and their applications
2007; Wiley; Volume: 75; Issue: 1 Linguagem: Inglês
10.1112/jlms/jdl002
ISSN1469-7750
Autores Tópico(s)Advanced Combinatorial Mathematics
ResumoJournal of the London Mathematical SocietyVolume 75, Issue 1 p. 18-34 Articles Generalizations of Ramanujan's reciprocity theorem and their applications Soon-Yi Kang, Soon-Yi Kang School of Mathematics, Korea Institute for Advanced Study, 207-43 Cheongnyangni 2-dong, Dongdaemun-gu, Seoul 130-722, Korea, [email protected]Search for more papers by this author Soon-Yi Kang, Soon-Yi Kang School of Mathematics, Korea Institute for Advanced Study, 207-43 Cheongnyangni 2-dong, Dongdaemun-gu, Seoul 130-722, Korea, [email protected]Search for more papers by this author First published: 08 January 2007 https://doi.org/10.1112/jlms/jdl002Citations: 17 2000 Mathematics Subject Classification 33D15, 11B65, 05A15. Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract First, we briefly survey Ramanujan's reciprocity theorem for a certain q-series related to partial theta functions and give a new proof of the theorem. Next, we derive generalizations of the reciprocity theorem that are also generalizations of the 1ψ1 summation formula and Jacobi triple product identity and show that these reciprocity theorems lead to generalizations of the quintuple product identity, as well. Last, we present some applications of the generalized reciprocity theorems and product identities, including new representations for generating functions for sums of six squares and those for overpartitions. Citing Literature Volume75, Issue1February 2007Pages 18-34 RelatedInformation
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