arXiv subjects
Publications and source records attributed to Sosuke Sasaki.
Let $k$ be a real quadratic field. Let $k_n$ be the $n$-th layer of the $\mathbb{Z}_2$-extension of $k$, and $2^{a_n}$ be the $2$-part of the class number of $k_n$. In this paper, we derive many laws concerning the sequence $(a_0,a_1,\dotsc)$, by iteratively extending the group of cyclotomic units.
The product formula of Artin symbols (norm residue symbols) is an important equality that connects local and global class field theory. Usually, the product formula of Artin symbols is considered in abelian extensions of global fields. In this paper, however, the product is considered in non-abelian extensions such that each symbol is well-defined. As an application, some properties on fundamental units of real quadratic fields are obtained and will be presented here.