Ramanujan ' s identities and representation of integers by certain binary and quaternary quadratic forms
| dc.citation.epage | 408 | en_US |
| dc.citation.issueNumber | 3 | en_US |
| dc.citation.spage | 375 | en_US |
| dc.citation.volumeNumber | 20 | en_US |
| dc.contributor.author | Berkovich, A. | en_US |
| dc.contributor.author | Yesilyurt, H. | en_US |
| dc.date.accessioned | 2016-02-08T10:01:16Z | |
| dc.date.available | 2016-02-08T10:01:16Z | |
| dc.date.issued | 2009 | en_US |
| dc.department | Department of Mathematics | en_US |
| dc.description.abstract | We revisit old conjectures of Fermat and Euler regarding the representation of integers by binary quadratic form x2+5y2. Making use of Ramanujan's 1ψ1 summation formula, we establish a new Lambert series identity for Σ∞n,m=-∞qn2+5m2 Conjectures of Fermat and Euler are shown to follow easily from this new formula. But we do not stop there. Employing various formulas found in Ramanujan's notebooks and using a bit of ingenuity, we obtain a collection of new Lambert series for certain infinite products associated with quadratic forms such as x2+6y2, 2x2+3y2, x2+15y2, 3x2+5y2, x2+27y2, x2+5(y2+z2+w2), 5x2+y2+z2+w2. In the process, we find many new multiplicative eta-quotients and determine their coefficients. © 2009 Springer Science+Business Media, LLC. | en_US |
| dc.identifier.doi | 10.1007/s11139-009-9215-8 | en_US |
| dc.identifier.eissn | 1572-9303 | |
| dc.identifier.issn | 1382-4090 | |
| dc.identifier.uri | http://hdl.handle.net/11693/22526 | |
| dc.language.iso | English | en_US |
| dc.publisher | Springer New York LLC | en_US |
| dc.relation.isversionof | http://dx.doi.org/10.1007/s11139-009-9215-8 | en_US |
| dc.source.title | Ramanujan Journal | en_US |
| dc.subject | Eta - quotients | en_US |
| dc.subject | Multiplicative functions | en_US |
| dc.subject | Q - series identities | en_US |
| dc.subject | Quadratic forms | en_US |
| dc.title | Ramanujan ' s identities and representation of integers by certain binary and quaternary quadratic forms | en_US |
| dc.type | Article | en_US |
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