Thue equations and the method of Chabauty-Coleman
Thue equations and the method of Chabauty-Coleman
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DOI：
10.1007/s002220100186
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发表时间：
2002-04
影响因子：
3.1
通讯作者：
Dino J. Lorenzini;T. Tucker
中科院分区：
文献类型：
--
作者：
Dino J. Lorenzini;T. Tucker
设 F (x, y)ε Z [x, y] 为 n 次齐次多项式，假设具有单位内容。设 h∈ Z 使得多项式 hzn− F (x, y) 在 Q [x, y, z] 中不可约。我们用 XF, h/Q 表示射影平面曲线 CF, h/Q 的非奇异完整模型，由方程 hzn− F (x, y)= 0 定义。经典的 Thue 方程是方程 F (x, y)= h，其中 F (x, 1) 没有重根。设 N (F, h) 表示集合 {(x, y)∈ Z2| 的基数F(x,y)=h且gcd(x,y)=1}。
Let F (x, y)∈ Z [x, y] be a homogenous polynomial of degree n, assumed to have unit content. Let h∈ Z be such that the polynomial hzn− F (x, y) is irreducible in Q [x, y, z]. We denote by XF, h/Q the nonsingular complete model of the projective plane curve CF, h/Q defined by the equation hzn− F (x, y)= 0. A classical Thue equation is an equation F (x, y)= h where F (x, 1) does not have repeated roots. Let N (F, h) denote the cardinality of the set {(x, y)∈ Z2| F (x, y)= h and gcd (x, y)= 1}.