论文标题
在与代数三角学相关的二元形式的基本区域
On the Area of the Fundamental Region of a Binary Form Associated with Algebraic Trigonometric Quantities
论文作者
论文摘要
令$ f（x，y）$为二进制学位的二进制形式，至少是三个和非零的判别。我们估计面积为curve $ | f（x，y）|的面积$ a_f $ |四个二进制形式家庭的= 1 $。我们感兴趣的前两个家庭是最低多项式的同质化，$ 2 \ cos \ left（\ frac {2π} {n} {n} \ right）$和$ 2 \ sin \ left（\ frac {2π} {2π} {n} {n} {n} {n} \ right）$我们认为的其余两个二进制形式的家族分别表示第一和第二类的Chebyshev多项式的均质化，分别表示$ t_n（x，y）$和$ u_n（x，y）$。
Let $F(x, y)$ be a binary form of degree at least three and non-zero discriminant. We estimate the area $A_F$ bounded by the curve $|F(x, y)| = 1$ for four families of binary forms. The first two families that we are interested in are homogenizations of minimal polynomials of $2\cos\left(\frac{2π}{n}\right)$ and $2\sin\left(\frac{2π}{n}\right)$, which we denote by $Ψ_n(x, y)$ and $Π_n(x, y)$, respectively. The remaining two families of binary forms that we consider are homogenizations of Chebyshev polynomials of first and second kinds, denoted $T_n(x, y)$ and $U_n(x, y)$, respectively.
