Higher order Fourier analysis as an algebraic theory I

Details Higher order Fourier analysis as an algebraic theory I Higher order Fourier analysis as an algebraic theory I

2009-03-05

arxiv.org/abs/0903.0897v1

Mathematics

Combinatorics

Scientific paper

Ergodic theory, Higher order Fourier analysis and the hyper graph regularity method are three possible approaches to Szemer\'edi type theorems in abelian groups. In this paper we develop an algebraic theory that creates a connection between these approaches. Our main method is to take the ultra product of abelian groups and to develop a precise algebraic theory of higher order characters on it. These results then can be turned back into approximative statements about finite Abelian groups.

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