4 papers
An inverse theorem for the Gowers -norm relative to quadratic level sets
Sean Prendiville
We prove an effective version of the inverse theorem for the Gowers -norm for functions supported on high-rank quadratic level sets in finite vector spaces. For configurations…
Extremal Sidon sets are Fourier uniform, with applications to partition regularity
Miquel Ortega, Sean Prendiville
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…
On the Ramsey number of the Brauer configuration
Jonathan Chapman, Sean Prendiville
We obtain a double exponential bound in Brauer's generalisation of van der Waerden's theorem, which concerns progressions with the same colour as their common difference. Such a re…
Rado's criterion over squares and higher powers
Sam Chow, Sofia Lindqvist, Sean Prendiville
We establish partition regularity of the generalised Pythagorean equation in five or more variables. Furthermore, we show how Rado's characterisation of a partition regular equatio…