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dc.contributor.authorBerkovich, A.en_US
dc.contributor.authorYesilyurt, H.en_US
dc.date.accessioned2016-02-08T10:01:16Z
dc.date.available2016-02-08T10:01:16Z
dc.date.issued2009en_US
dc.identifier.issn1382-4090
dc.identifier.urihttp://hdl.handle.net/11693/22526
dc.description.abstractWe 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.language.isoEnglishen_US
dc.source.titleRamanujan Journalen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s11139-009-9215-8en_US
dc.subjectEta - quotientsen_US
dc.subjectMultiplicative functionsen_US
dc.subjectQ - series identitiesen_US
dc.subjectQuadratic formsen_US
dc.titleRamanujan ' s identities and representation of integers by certain binary and quaternary quadratic formsen_US
dc.typeArticleen_US
dc.departmentDepartment of Mathematicsen_US
dc.citation.spage375en_US
dc.citation.epage408en_US
dc.citation.volumeNumber20en_US
dc.citation.issueNumber3en_US
dc.identifier.doi10.1007/s11139-009-9215-8en_US
dc.publisherSpringer New York LLCen_US
dc.identifier.eissn1572-9303


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