Sato, Hiroki On class number formula for the real quadratic fields. (English) Zbl 1068.11072 Proc. Japan Acad., Ser. A 80, No. 7, 129-130 (2004). Let \(d\) be the discriminant of a real quadratic number field with fundamental unit \(\varepsilon\), and class number \(h\), and \(\chi\) the associated Dirichlet character. Then the author proves the class number formula \(h = [\sqrt{d}/(2 \log \varepsilon) \cdot \sum_{n=1}^{[d/2]} \chi(n)/n]\). Reviewer: Franz Lemmermeyer (Bilkent) MSC: 11R29 Class numbers, class groups, discriminants 11R11 Quadratic extensions Keywords:real quadratic fields; class number formula PDF BibTeX XML Cite \textit{H. Sato}, Proc. Japan Acad., Ser. A 80, No. 7, 129--130 (2004; Zbl 1068.11072) Full Text: DOI Euclid OpenURL References: [1] Apostol, T. M.: Introduction to Analytic Number Theory. Undergraduate Texts in Mathematics. Springer-Verlag, New York-Berlin-Heidelberg-Tokyo (1976). · Zbl 0335.10001 [2] Cohn, H.: Advanced Number Theory. Dover Books on Advanced Mathematics. Dover, New York (1980). · Zbl 0474.12002 [3] Leu, M.-G.: On \(L(1, \chi)\) and class number formula for the real quadratic fields. Proc. Japan Acad., 72A , 69-74 (1996). · Zbl 0868.11037 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.