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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.
##### MSC:
 11R29 Class numbers, class groups, discriminants 11R11 Quadratic extensions