{"month":"04","_id":"216","day":"15","type":"journal_article","page":"545 - 578","abstract":[{"text":"For any N ≥ 2, let Z ⊂ ℙN be a geometrically integral algebraic variety of degree d. This article is concerned with the number Nz(B) of ℚ-rational points on Z which have height at most B. For any ε > 0, we establish the estimate NZ(B) = O d,ε,N(Bdim Z+ε), provided that d ≥ 6. As indicated, the implied constant depends at most on d, ε, and N.","lang":"eng"}],"date_updated":"2021-01-12T06:55:41Z","title":"Counting rational points on algebraic varieties","date_created":"2018-12-11T11:45:15Z","publist_id":"7696","publication":"Duke Mathematical Journal","citation":{"short":"T.D. Browning, R. Heath Brown, P. Salberger, Duke Mathematical Journal 132 (2006) 545–578.","ista":"Browning TD, Heath Brown R, Salberger P. 2006. Counting rational points on algebraic varieties. Duke Mathematical Journal. 132(3), 545–578.","chicago":"Browning, Timothy D, Roger Heath Brown, and Per Salberger. “Counting Rational Points on Algebraic Varieties.” Duke Mathematical Journal. Unknown, 2006. https://doi.org/10.1215/S0012-7094-06-13236-2.","mla":"Browning, Timothy D., et al. “Counting Rational Points on Algebraic Varieties.” Duke Mathematical Journal, vol. 132, no. 3, Unknown, 2006, pp. 545–78, doi:10.1215/S0012-7094-06-13236-2.","ama":"Browning TD, Heath Brown R, Salberger P. Counting rational points on algebraic varieties. Duke Mathematical Journal. 2006;132(3):545-578. doi:10.1215/S0012-7094-06-13236-2","ieee":"T. D. Browning, R. Heath Brown, and P. Salberger, “Counting rational points on algebraic varieties,” Duke Mathematical Journal, vol. 132, no. 3. Unknown, pp. 545–578, 2006.","apa":"Browning, T. D., Heath Brown, R., & Salberger, P. (2006). Counting rational points on algebraic varieties. Duke Mathematical Journal. Unknown. https://doi.org/10.1215/S0012-7094-06-13236-2"},"extern":1,"volume":132,"status":"public","doi":"10.1215/S0012-7094-06-13236-2","publisher":"Unknown","issue":"3","date_published":"2006-04-15T00:00:00Z","intvolume":" 132","quality_controlled":0,"publication_status":"published","author":[{"orcid":"0000-0002-8314-0177","full_name":"Timothy Browning","first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Heath-Brown, Roger","last_name":"Heath Brown","first_name":"Roger"},{"first_name":"Per","last_name":"Salberger","full_name":"Salberger, Per"}],"year":"2006"}