Density of rational points on diagonal quartic surfaces
نویسندگان
چکیده
منابع مشابه
Density of Rational Points on Diagonal Quartic Surfaces
Let a, b, c, d be nonzero rational numbers whose product is a square, and let V be the diagonal quartic surface in P defined by ax + by + cz + dw = 0. We prove that if V contains a rational point that does not lie on any of the 48 lines on V or on any of the coordinate planes, then the set of rational points on V is dense in both the Zariski topology and the real analytic
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Let n ≥ 3 be an integer and let F (x) = F (x1, . . . , xn) ∈ Z[x1, . . . , xn] be an absolutely irreducible form of degree d, producing a hypersurface of dimension n − 2 in Pn−1. This paper is primarily concerned with the number of rational points on this hypersurface, of height at most B, say. In order to describe such points we choose representatives x = (x1, . . . , xn) ∈ Z with the xi not a...
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2010
ISSN: 1944-7833,1937-0652
DOI: 10.2140/ant.2010.4.1