On class number formula for the real quadratic fields. (English) Zbl 1068.11072

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 \(h = [\sqrt{d}/(2 \log \varepsilon) \cdot \sum_{n=1}^{[d/2]} \chi(n)/n]\).


11R29 Class numbers, class groups, discriminants
11R11 Quadratic extensions
Full Text: DOI Euclid


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