On arithmetic of certain matrix algebras
The purpose of this paper is to develop the arithmetic of \(\mathbb{Z}(\zeta)\) and the ideal class semigroups \({\mathcal G}\), as done earlier in [\textit{C. G. Latimer} and \textit{C. C. MacDuffee}, Ann. Math., II. Ser. 34, 313-316 (1933; Zbl 0006.29002); \textit{H. Midorikawa} (preprint); \textit{O. Taussky}, Can. J. Math. 1, 300-302 (1949; Zbl 0045.15404)], and to introduce Dirichlet series in order to calculate \(|{\mathcal G}|\) as well. Besides definitions and statements of theorems, or so, there are no proofs. The theorems apparently connect \(\zeta\)-functions, \(L\)-functions, class-numbers, order of unit groups, discriminants etc.
scientific article; zbMATH DE number 799713
scientific article