Elliptic modular invariants of 4-by-4 matrices

被引：0
|
作者：
Chien, Mao -Ting [1 ]
Nakazato, Hiroshi [2 ]
机构：
[1] Soochow Univ, Dept Math, Taipei 11102, Taiwan
[2] Hirosaki Univ, Fac Sci & Technol, Hirosaki 0368561, Japan
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2023年 / 662卷
关键词：
Modular invariant; Elliptic curve; Numerical range; NUMERICAL RANGES;
D O I：
10.1016/j.laa.2022.12.025
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let A be an n-by -n matrix. The ternary form FA(t, x, y) = det(tIn + xR(A) + y(sic)(A)) characterizes the numerical range of A. For n = 4, we assume that the ternary form FA(t, x, y) is irreducible and the complex projective algebraic curve FA(t, x, y) = 0 is elliptic. We prove that the number of analytic curves composing the real algebraic curve of F-A(t, x, y) = 0 is 2. This result is applied to show that the j-invariant of the elliptic curve F-A(t, x, y) = 0 is greater than or equal to 1. (c) 2023 Elsevier Inc. All rights reserved.
引用
收藏
页码：49 / 66
页数：18
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