Indivisibility of relative class numbers of totally imaginary quadratic extensions and vanishing of these relative Iwasawa invariants
Indivisibility of relative class numbers of totally imaginary quadratic extensions and vanishing of these relative Iwasawa invariants
复制标题
全虚二次扩张的相对类数的不可分性以及这些相对岩泽不变量的消失
DOI：
10.1016/j.jnt.2017.09.024
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发表时间：
2018
影响因子：
0.7
通讯作者：
Takai Yuuki
中科院分区：
文献类型：
--
作者：
Okazaki Ryota;Yanagawa Kohji;Takai Yuuki
我们研究了 CM 域的相对类数的不可分性问题。对于素数 p > 3，Kohnen-Ono 通过使用半积分权重的模形式给出了类数与 p 素数的虚二次域数量的下界。我们将他们的方法推广到希尔伯特模形式，并给出了 CM 二次扩展 K/F 的数量下界，对于全实数域 F，其相对类数与 p 素数，F 是 Q 上的伽罗瓦且足够大的素数 p。将不可分性结果与 p 的分解条件相结合，我们给出了相对 Iwasawa 不变量消失的结果。
We study an indivisibility problem of the relative class numbers of CM fields. For prime p> 3, Kohnen–Ono gave a lower bound of the number of the imaginary quadratic fields whose class numbers are prime to p by using modular forms of half-integral weight. We generalize their method to Hilbert modular forms and give a lower bound of the number of CM quadratic extensions K/F whose relative class numbers prime to p for totally real number field F which is Galois over Q and sufficiently large prime p. Combining the indivisibility result with the decomposition condition of p, we show a result on vanishing of relative Iwasawa invariants.