Rational approximation to real points on quadratic hypersurfaces
نویسندگان
چکیده
منابع مشابه
Rational quadratic approximation to real algebraic curves
An algorithm is proposed to give a global approximation of an implicit real plane algebraic curve with rational quadratic B-spline curves. The algorithm consists of four steps: topology determination, curve segmentation, segment approximation and curve tracing. Due to the detailed geometric analysis, high accuracy of approximation may be achieved with a small number of quadratic segments. The f...
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Let f(x) = x+ax+bx+cx ∈ Z[x] and consider the hypersurface of degree five given by the equation Vf : f(p) + f(q) = f(r) + f(s). Under the assumption b 6= 0 we show that there exists Q-unirational elliptic surface contained in Vf . If b = 0, a < 0 and −a 6≡ 2, 18, 34 (mod 48) then there exists Q-rational surface contained in Vf . Moreover, we prove that for each f of degree five there exists Q(i...
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R0<b162R0 gcd(b1, N )1/2 R 0 (HP) . The second line is false and in fact one has M1 = 1 in Proposition 3. The author is very grateful to Professor Hongze Li for drawing his attention to this flaw. The error can be fixed by introducing an average over b1 into the statement of Proposition 3. This allows us to recover the main theorem in [1], and also [2, Lemma 11], via the following modification....
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2020
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms.12388