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arXiv · 2012.13274

On the Area of the Fundamental Region of a Binary Form Associated with Algebraic Trigonometric Quantities

Anton Mosunov
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Abstract

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 $2\cos\left(\frac{2\pi}{n}\right)$ and $2\sin\left(\frac{2\pi}{n}\right)$, which we denote by $\Psi_n(x, y)$ and $\Pi_n(x, y)$, 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.

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Anton Mosunov. 2020-12-24. On the Area of the Fundamental Region of a Binary Form Associated with Algebraic Trigonometric Quantities. https://doi.org/10.1112/mtk.12087

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