Extremal Sidon sets are Fourier uniform, with applications to partition regularity
Abstract
Generalising results of ErdősFreud 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 Fourierpseudorandom, in that they have no large nontrivial 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.13447
 Bibcode:
 2021arXiv211013447O
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Number Theory