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

页码：49 / 66

页数：18

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