Lee, Seok-Min; Ono, Takashi On a certain invariant for real quadratic fields. (English) Zbl 1161.11392 Proc. Japan Acad., Ser. A 79, No. 8, 119-122 (2003). Summary: This article is a continuation and completion of the second author’s paper [Proc. Japan Acad., Ser. A 79, No. 4, 95–97 (2003; Zbl 1099.11029)]. Let \(K = \mathbb Q(\sqrt{m})\) be a real quadratic field, \(\mathcal O_K\) its ring of integers and \(G = \text{Gal}(K/\mathbb Q)\). For \(\gamma \in H^1(G, \mathcal O_K^{\times})\), we associate a module \(M_c/P_c\) for \(\gamma = [c]\). It is known that \(M_c/P_c \approx \mathbb Z/\Delta_m \mathbb Z\) where \(\Delta_m = 1\) or 2 and we determine \(\Delta_m\). Cited in 2 Documents MSC: 11R11 Quadratic extensions 11F75 Cohomology of arithmetic groups 11R27 Units and factorization PDF BibTeX XML Cite \textit{S.-M. Lee} and \textit{T. Ono}, Proc. Japan Acad., Ser. A 79, No. 8, 119--122 (2003; Zbl 1161.11392) Full Text: DOI References: [1] Ono, T.: A Note on Poincaré sums for finite groups. Proc. Japan Acad., 79A , 95-97 (2003). · Zbl 1099.11029 · doi:10.3792/pjaa.79.95 [2] Stark, H. M.: An Introduction to Number Theory. The MIT Press, Cambridge, Massachusetts-London, England (1978). · Zbl 0412.03033 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.