Matsusaka Toshiki, Ueki Jun
Faculty of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka-shi, 819-0395 Fukuoka Japan.
Department of Mathematics, Faculty of Science, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, 112-8610 Tokyo Japan.
Res Math Sci. 2023;10(1):4. doi: 10.1007/s40687-022-00366-8. Epub 2022 Dec 9.
É. Ghys proved that the linking numbers of modular knots and the "missing" trefoil in coincide with the values of a highly ubiquitous function called the Rademacher symbol for . In this article, we replace by the triangle group for any coprime pair (, ) of integers with . We invoke the theory of harmonic Maass forms for to introduce the notion of the Rademacher symbol , and provide several characterizations. Among other things, we generalize Ghys's theorem for modular knots around any "missing" torus knot in and in a lens space.
É. 吉斯证明了模纽结的环绕数以及 中的“缺失”三叶结与一个被称为 的拉德马赫符号的高度普遍存在的函数的值一致。在本文中，对于任意互质的整数对(, )且 ，我们用三角形群 代替 。我们借助 的调和马阿斯形式理论引入拉德马赫符号 的概念，并给出几种刻画。特别地，我们将吉斯关于模纽结的定理推广到 以及透镜空间中任意“缺失”的环面纽结周围。
