【研究發展處訊】
數學系簡茂丁講座教授發表最新期刊論文
Elliptic modular invariants of 4-by-4 matrices
作者:Chien, Mao -Ting ; Nakazato, Hiroshi
LINEAR ALGEBRA AND ITS APPLICATIONS (SCI)
卷冊:662
頁碼:49-66
DOI:10.1016/j.laa.2022.12.025
出版日期:APR 1 2023
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.
設A為n階方陣。三元式 F(t,x,y) = det(tI + x Re(A) + y Im(A)) 可刻劃矩陣A 的數值域。對於 n =4,假設三元式 F(t,x,y) 是不可約的,且其複數射影代數曲線 F(t,x,y) =0 是橢圓曲線。我們證明了F(t,x,y)=0的實數代數曲線的解析曲線的條數為2。應用該結果證明橢圓曲線F(t,x,y)=0的j-不變量至少是1。
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