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Counting rational points on algebraic varieties
T. D. Browning, D. R. Heath-Brown, P. Salberger
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Source: Crossref
Published: Apr 15, 2006
DOI: 10.1215/s0012-7094-06-13236-2
Open original source ↗Source 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)=Od,ε,N(BdimZ+ε), provided that d,ε. As indicated, the implied constant depends at most on d,ε, and N
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