NORTHCOTT THEOREM ON HEIGHTS .1. A GENERAL ESTIMATE
NORTHCOTT THEOREM ON HEIGHTS .1. A GENERAL ESTIMATE
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DOI：
10.1007/bf01311215
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发表时间：
1993-01-01
影响因子：
0.9
通讯作者：
SCHMIDT, WM
中科院分区：
文献类型：
--
作者：
SCHMIDT, WM
给定点P =（α 0：.其中A是代数数域，d（P）是它的度，H（P）是它的绝对乘法高度。Northcott定理指出，给定d，n和X，只有n个点P是P（n）的元素，d（P）小于或等于d，H（P）小于或等于X。我们将证明至多存在c（d，n）X（d（d + n））这样的点。
Given a point P = (alpha0: ... : alpha(n)) of projective space P(n) = P(n)(A) where A is the field of algebraic numbers, let d(P) be its degree and H(P) its absolute multiplicative height. Northcott's Theorem says that given d, n and X, there are only finitely many points P is-an-element-of P(n) with d(P) less-than-or-equal-to d and H(P) less-than-or-equal-to X. We will show that there are at most c(d, n)X(d(d + n)) such points.