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

Miquel Ortega, Sean Prendiville

• Generalising results of Erd˝os-Freud and Lindstr¨om, we prove that the largest Sidonsubset of a bounded interval of integers is equidistributed in Bohr neighbourhoods. Weestablish this by showing that extremal Sidon sets are Fourier-pseudorandom, in that theyhave no large non-trivial Fourier coefficients. As a further application we deduce that, forany partition regular equation in five or more variables, every finite colouring of an extremalSidon set has a monochromatic solution.