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 Author Doyle, Gregory Title Quadratic Form Gauss Sums URL http://www.collectionscanada.gc.ca/obj/thesescanada/vol2/OOCC/TC-OOCC-25657.pdf  https://curve.carleton.ca/system/files/etd/6245016a-490e-4f76-a439-039e0a1e4496/etd_pdf/cfafb7cb1efac0137cd6257dc461c994/doyle-quadraticformgausssums.pdf  https://curve.carleton.ca/6245016a-490e-4f76-a439-039e0a1e4496 Publication Date 2016 Degree PhD Discipline/Department Pure Mathematics Degree Level doctoral University/Publisher Carleton University Abstract Let p be a prime, n, r positive integers, S an integer coprime to p. We let Q_r denote an r-dimensional integral quadratic form. For convenience, set e(x) = e^{2 pi i x}, where x is any rational number, i is the imaginary unit. Denote the quadratic Gauss sum by G(S;p^n). The evaluation of this sum was completed by Gauss in the early 19th century. Many proofs of these results have subsequently been obtained through a variety of methods. We are interested in the so called quadratic form Gauss sum, given by G(Q_r;S;p^n) - \sum_{x_1, x_2, ..., x_r}^{p^n-1} e(S/p^n * Q_r). Under certain assumptions on Q_r, we show how we may express G(Q_r;S;p^n) as a product of quadratic Gauss sums. Country of Publication ca Format application/pdf Record ID oai:collectionscanada.gc.ca:OOCC.25657 Other Identifiers TC-OOCC-25657 Repository canada Date Indexed 2017-01-03 Grantor Carleton University