Rado's criterion over squares and higher powers

Chow, Sam and Lindqvist, Sofia and Prendiville, Sean (2019) Rado's criterion over squares and higher powers. Journal of the European Mathematical Society. 0-0. ISSN 1435-9855 (In Press)

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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 equation remains valid over the set of positive kth powers, provided the equation has at least (1+o(1))klogk variables. We thus completely describe which diagonal forms are partition regular and which are not, given sufficiently many variables. In addition, we prove a supersaturated version of Rado's theorem for a linear equation restricted either to squares minus one or to logarithmically-smooth numbers.

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Journal Article
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Journal of the European Mathematical Society
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27 Sep 2019 14:15
In Press
Last Modified:
27 Jan 2022 09:33