ARITHMETIC PROGRESSIONS - AN OPERATOR THEORETIC VIEW

摘要

Motivated by the recent Green-Tao theorem on arithmetic progressions in the primes, we discuss some of the basic operator theoretic techniques used in its proof. In particular, we obtain a complete proof of Sze-meredi's theorem for arithmetic progressions of length 3 (Roth's theorem) and the Furstenberg-Sarkozy theorem.