论文标题
在某些模块化曲线上的点生成的数字字段中分裂数字字段
Splitting of primes in number fields generated by points on some modular curves
论文作者
论文摘要
我们研究了模块化曲线上点产生的数字场中的素数。 Momose是第一个注意到$ x_1（n）$上的二次点生成二次字段，某些素数以特定方式分裂，后来Krumm扩大了他的结果。我们证明了关于由点曲线上的点生成的二次字段中素数的分裂行为$ x_0（n）$（$ n = 37 $）以及在$ x_1（2，14）$上生成的立方字段的$ x_0（n）$。
We study the splitting of primes in number fields generated by points on modular curves. Momose was the first to notice that quadratic points on $X_1(n)$ generate quadratic fields over which certain primes split in a particular way and his results were later expanded upon by Krumm. We prove results about the splitting behaviour of primes in quadratic fields generated by points on the modular curves $X_0(n)$ which are hyperelliptic (except for $n=37$) and in cubic fields generated by points on $X_1(2, 14)$.
