The Library
Rado's criterion over squares and higher powers
Tools
Chow, Sam, Lindqvist, Sofia and Prendiville, Sean (2021) Rado's criterion over squares and higher powers. Journal of the European Mathematical Society, 23 (6). pp. 1925-1997. doi:10.4171/JEMS/1047 ISSN 1435-9855.
|
PDF
WRAP-Rado's-criterion-over-squares-higher-powers-Chow-2019.pdf - Accepted Version - Requires a PDF viewer. Download (981Kb) | Preview |
Official URL: https://doi.org/10.4171/JEMS/1047
Abstract
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))k log k 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.
Item Type: | Journal Article | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Combinatorial analysis, Ramsey theory | ||||||||||||
Journal or Publication Title: | Journal of the European Mathematical Society | ||||||||||||
Publisher: | European Mathematical Society Publishing House | ||||||||||||
ISSN: | 1435-9855 | ||||||||||||
Official Date: | 16 February 2021 | ||||||||||||
Dates: |
|
||||||||||||
Volume: | 23 | ||||||||||||
Number: | 6 | ||||||||||||
Page Range: | pp. 1925-1997 | ||||||||||||
DOI: | 10.4171/JEMS/1047 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Reuse Statement (publisher, data, author rights): | To appear Journal of the European Mathematical Society | ||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
Date of first compliant deposit: | 18 October 2019 | ||||||||||||
Date of first compliant Open Access: | 23 October 2019 | ||||||||||||
RIOXX Funder/Project Grant: |
|
||||||||||||
Related URLs: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year