Aritmetik dizilerde Roth teoremi

This thesis aims to give two different proofs of Roth's theorem on arithmetic progressions, which is one of the most important results in additive combinatorics. This theorem guarantees the existence of 3-term arithmetic progressions in sufficiently large subsets of the set of positive integers. Aforementioned result was first proved by Klaus Roth in 1953. Roth's original proof is based on the Fourier analysis techniques. We will first give the graph-theoretical proof and then the finite Fourier analytic proof of Roth's theorem on arithmetic progressions.