Counting rational points on hypersurfaces Browning, Timothy D ; https://orcid.org/0000-0002-8314-0177 Heath Brown, Roger For any n ≧ 2, let F ∈ ℤ [ x 1, … , xn ] be a form of degree d≧ 2, which produces a geometrically irreducible hypersurface in ℙn–1. This paper is concerned with the number N(F;B) of rational points on F = 0 which have height at most B. For any ε &gt; 0 we establish the estimate N(F; B) = O(B n− 2+ ε ), whenever either n ≦ 5 or the hypersurface is not a union of lines. Here the implied constant depends at most upon d, n and ε. Walter de Gruyter and Co 2005 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/212 Browning TD, Heath Brown R. Counting rational points on hypersurfaces. <i>Journal fur die Reine und Angewandte Mathematik</i>. 2005;(584):83-115. doi:<a href="https://doi.org/10.1515/crll.2005.2005.584.83">https://doi.org/10.1515/crll.2005.2005.584.83</a> eng info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1515/crll.2005.2005.584.83 info:eu-repo/semantics/altIdentifier/issn/0075-4102 info:eu-repo/semantics/altIdentifier/arxiv/abs/math/0404456 info:eu-repo/semantics/openAccess