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Harmonic analysis of Rajchman algebras
(University of Waterloo, 2010-08-31)
Abstract harmonic analysis is mainly concerned with the study of locally compact groups, their unitary representations, and the function spaces associated with them. The Fourier and Fourier-Stieltjes algebras are two of ...
Upper Bounds for the Number of Integral Points on Quadratic Curves and Surfaces
(University of Waterloo, 2010-04-27)
We are interested in investigating the number of integral points on quadrics. First, we consider non-degenerate plane conic curves defined over Z. In particular we look at two types of conic sections: hyperbolas with ...
Asymptotic Estimates for Rational Spaces on Hypersurfaces in Function Fields
(University of Waterloo, 2010-06-29)
The ring of polynomials over a finite field has many arithmetic properties similar to those of the ring of rational integers. In this thesis, we apply the Hardy-Littlewood circle method to investigate the density of rational ...