Improvements in Birch's theorem on forms in many variables Browning, Timothy D ; https://orcid.org/0000-0002-8314-0177 Prendiville, Sean We show that a non-singular integral form of degree d is soluble non-trivially over the integers if and only if it is soluble non-trivially over the reals and the p-adic numbers, provided that the form has at least (d-\sqrt{d}/2)2^d variables. This improves on a longstanding result of Birch. Walter de Gruyter 2015 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/271 Browning TD, Prendiville S. Improvements in Birch’s theorem on forms in many variables. <i>Journal fur die Reine und Angewandte Mathematik</i>. 2017(731):203-234. doi:<a href="https://doi.org/10.1515/crelle-2014-0122">10.1515/crelle-2014-0122</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1515/crelle-2014-0122 info:eu-repo/semantics/altIdentifier/issn/0075-4102 info:eu-repo/semantics/altIdentifier/arxiv/1402.4489 info:eu-repo/semantics/openAccess