{"publisher":"Unknown","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 &gt; 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"}],"month":"04","author":[{"full_name":"Timothy Browning","orcid":"0000-0002-8314-0177","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"},{"last_name":"Salberger","first_name":"Per","full_name":"Salberger, Per"}],"citation":{"mla":"Browning, Timothy D., et al. “Counting Rational Points on Algebraic Varieties.” <i>Duke Mathematical Journal</i>, vol. 132, no. 3, Unknown, 2006, pp. 545–78, doi:<a href=\"https://doi.org/10.1215/S0012-7094-06-13236-2\">10.1215/S0012-7094-06-13236-2</a>.","apa":"Browning, T. D., Heath Brown, R., &#38; Salberger, P. (2006). Counting rational points on algebraic varieties. <i>Duke Mathematical Journal</i>. Unknown. <a href=\"https://doi.org/10.1215/S0012-7094-06-13236-2\">https://doi.org/10.1215/S0012-7094-06-13236-2</a>","ieee":"T. D. Browning, R. Heath Brown, and P. Salberger, “Counting rational points on algebraic varieties,” <i>Duke Mathematical Journal</i>, vol. 132, no. 3. Unknown, pp. 545–578, 2006.","ista":"Browning TD, Heath Brown R, Salberger P. 2006. Counting rational points on algebraic varieties. Duke Mathematical Journal. 132(3), 545–578.","ama":"Browning TD, Heath Brown R, Salberger P. Counting rational points on algebraic varieties. <i>Duke Mathematical Journal</i>. 2006;132(3):545-578. doi:<a href=\"https://doi.org/10.1215/S0012-7094-06-13236-2\">10.1215/S0012-7094-06-13236-2</a>","chicago":"Browning, Timothy D, Roger Heath Brown, and Per Salberger. “Counting Rational Points on Algebraic Varieties.” <i>Duke Mathematical Journal</i>. Unknown, 2006. <a href=\"https://doi.org/10.1215/S0012-7094-06-13236-2\">https://doi.org/10.1215/S0012-7094-06-13236-2</a>.","short":"T.D. Browning, R. Heath Brown, P. Salberger, Duke Mathematical Journal 132 (2006) 545–578."},"title":"Counting rational points on algebraic varieties","page":"545 - 578","date_published":"2006-04-15T00:00:00Z","date_created":"2018-12-11T11:45:15Z","issue":"3","type":"journal_article","publication":"Duke Mathematical Journal","doi":"10.1215/S0012-7094-06-13236-2","date_updated":"2021-01-12T06:55:41Z","status":"public","day":"15","extern":1,"year":"2006","_id":"216","publication_status":"published","quality_controlled":0,"volume":132,"publist_id":"7696","intvolume":"       132"}