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On the class number formula of certain real quadratic fields. (English) Zbl 1294.11198
The class number formula is a well-known equality involving the class number \(h_K\) of a number field \(K\), some other arithmetical invariants and the residue of the Dedekind zeta function at the pole \(s=1\). Several authors have obtained alternative expressions for \(h_K\) in the attempt to find formulas not involving transcendental terms. In the paper under review some results of [P. Chowla, J. Reine Angew. Math. 230, 51–60 (1968; Zbl 0155.38002)] are generalized to real quadratic fields with discriminant \(d \equiv 5 \pmod{8}\), dropping the assumption that \(d\) is prime.
11R29 Class numbers, class groups, discriminants
11R11 Quadratic extensions