# Extremal Sidon sets are Fourier uniform, with applications to partition regularity

@inproceedings{Ortega2021ExtremalSS, title={Extremal Sidon sets are Fourier uniform, with applications to partition regularity}, author={Miquel Ortega and Sean Prendiville}, year={2021} }

Generalising results of Erdős-Freud and Lindström, we prove that the largest Sidon subset of a bounded interval of integers is equidistributed in Bohr neighbourhoods. We establish this by showing that extremal Sidon sets are Fourier-pseudorandom, in that they have no large non-trivial Fourier coefficients. As a further application we deduce that, for any partition regular equation in five or more variables, every finite colouring of an extremal Sidon set has a monochromatic solution.

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