HEIGHTS OF POINTS ON ELLIPTIC CURVES OVER Q

被引：3

作者：

Griffin, Michael ^{[1
]}

Ono, Ken ^{[2
]}

Tsai, Wei-Lun ^{[2
]}

机构：

[1] Brigham Young Univ, Dept Math, 275 TMCB, Provo, UT 84602 USA

[2] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 149卷 / 12期

关键词：

CANONICAL HEIGHT; LOWER BOUNDS;

D O I：

10.1090/proc/15605

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note we obtain effective lower bounds for the canonical heights of non-torsion points on E(Q) by making use of suitable elliptic curve ideal class pairings Psi(E,-D ): E(Q) x E-D(Q) bar right arrow CL(-D). In terms of the class number H(-D) and T-E(-D), a logarithmic function in D, we prove (h) over cap (P) > vertical bar E-tor(Q)vertical bar(2)/(H(-D) + vertical bar E-tor(Q)vertical bar)(2).T-E(-D).( )

引用

页码：5093 / 5100

页数：8

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