File:Rado's criterion over squares and higher powers.pdf

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English: 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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Source Content available at arxiv.org (Dedicated link) (archive.org link)
Author Rado's criterion over squares and higher powers

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current07:57, 11 November 2018Thumbnail for version as of 07:57, 11 November 20181,133 × 1,593, 72 pages (772 KB)Acagastya (talk | contribs)User created page with UploadWizard

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