--- res: bibo_abstract: - We show that any subset of the squares of positive relative upper density contains nontrivial solutions to a translation-invariant linear equation in five or more variables, with explicit quantitative bounds. As a consequence, we establish the partition regularity of any diagonal quadric in five or more variables whose coefficients sum to zero. Unlike previous approaches, which are limited to equations in seven or more variables, we employ transference technology of Green to import bounds from the linear setting.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Timothy D foaf_name: Browning, Timothy D foaf_surname: Browning foaf_workInfoHomepage: http://www.librecat.org/personId=35827D50-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-8314-0177 - foaf_Person: foaf_givenName: Sean foaf_name: Prendiville, Sean foaf_surname: Prendiville bibo_doi: 10.1093/imrn/rnw096 bibo_issue: '7' bibo_volume: 2017 dct_date: 2017^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/1073-7928 dct_language: eng dct_publisher: Oxford University Press@ dct_title: A transference approach to a Roth-type theorem in the squares@ ...