Counting rational points on algebraic varieties

T.D. Browning, R. Heath Brown, P. Salberger, Duke Mathematical Journal 132 (2006) 545–578.

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Abstract
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.
Publishing Year
Date Published
2006-04-15
Journal Title
Duke Mathematical Journal
Volume
132
Issue
3
Page
545 - 578
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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
Browning, T. D., Heath Brown, R., & Salberger, P. (2006). Counting rational points on algebraic varieties. Duke Mathematical Journal, 132(3), 545–578. https://doi.org/10.1215/S0012-7094-06-13236-2
Browning, Timothy D, Roger Heath Brown, and Per Salberger. “Counting Rational Points on Algebraic Varieties.” Duke Mathematical Journal 132, no. 3 (2006): 545–78. https://doi.org/10.1215/S0012-7094-06-13236-2.
T. D. Browning, R. Heath Brown, and P. Salberger, “Counting rational points on algebraic varieties,” Duke Mathematical Journal, vol. 132, no. 3, pp. 545–578, 2006.
Browning TD, Heath Brown R, Salberger P. 2006. Counting rational points on algebraic varieties. Duke Mathematical Journal. 132(3), 545–578.
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.

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