On the number of representations by quadratic forms and triangular numbers

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dc.contributor.authorTotani, Yash
dc.contributor.authorUniversity of Lethbridge. Faculty of Arts and Science
dc.contributor.supervisorAkbary-Majdabadno, Amir
dc.date.accessioned2021-12-06T22:05:25Z
dc.date.available2021-12-06T22:05:25Z
dc.date.issued2021
dc.degree.levelMastersen_US
dc.description.abstractIn this thesis, we study the problem of representing integers by quadratic forms. The formulas for the number of representations are obtained as a sum of an Eisenstein part and a cusp part. We begin by solving the representation problem for binary quadratic forms of discriminant -D<0 where the number field Q(√−D) has class number 3. We obtain formulas for the number of representations of an integer as a sum of k triangular numbers, denoted by δk(n), for even values of k. As special cases, for k=14,16 and 18, new formulas are provided in which the cusp part is given as a linear combination of certain eta products. At the end, for even values of k, we study the first and the second moments of δk(n) and prove an analogue of the Wagon's conjecture for the second moment of δk(n).en_US
dc.identifier.urihttps://hdl.handle.net/10133/6104
dc.language.isoen_USen_US
dc.proquest.subject0405en_US
dc.proquestyesYesen_US
dc.publisherLethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Scienceen_US
dc.publisher.departmentDepartment of Mathematics and Computer Scienceen_US
dc.publisher.facultyArts and Scienceen_US
dc.relation.ispartofseriesThesis (University of Lethbridge. Faculty of Arts and Science)en_US
dc.subjectnumber theoryen_US
dc.subjectquadratic formsen_US
dc.subjecttriangular numbersen_US
dc.subjectNumber theoryen_US
dc.subjectForms, Quadraticen_US
dc.subjectDissertations, Academicen_US
dc.titleOn the number of representations by quadratic forms and triangular numbersen_US
dc.typeThesisen_US
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