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Fourier analytic applications to number theory Hamel, Mariah

Abstract

In this paper we give expositions of Roth's theorem, Weyl's inequality and Vinogradov's three-primes theorem. In the proofs, we will frequently use exponential sums and more specifically the discrete Fourier transform. In the proof of Vinogradov's three-primes theorem we will use Hardy and Littlewood's circle method. This paper is intended to be self-contained and will hopefully be readable to someone with little background in the area.

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