Plane curves of degree $2n$ with three $n$-tuple points
نویسندگان
چکیده
منابع مشابه
Constructions of Plane Curves with Many Points
In this paper we investigate some plane curves with many points over Q, finite fields and cyclotomic fields. In a previous paper [4] the first two authors constructed a sequence of absolutely irreducible polynomials Pd(x, y) ∈ Z[x, y] of degree d having low height and many integral solutions to Pd(x, y) = 0. (The definition of these polynomials will be recalled in §4.) Here we construct further...
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This curve has the points (1 : 0 : 0) and (0 : 1 : 0) at infinity over any field. The affine equation is XY +Y +X = 0. The origin is a point of this curve. If (x, y) ∈ F8 is a point of this curve with nonzero coordinates, then x = 1. So 0 = xy + y + x = xy + xy + x = x[(xy) + (xy) + 1]. Let t = xy. Then t + t+ 1 = 0. So the Klein quartic has 3.7 = 21 rational points over F8 with nonzero coordin...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky a fysiky
سال: 1917
ISSN: 1802-114X
DOI: 10.21136/cpmf.1917.123718