Exponents of class groups of complex quadratic fields. (English) Zbl 0217.04202

Let \(E(-d)\) denote the exponent of the class group of the complex quadratic field \(\mathbb Q(\sqrt{-d})\), where \(-d\) is the discriminant of the field. It is known that there is at most one \(d>5460\) such that \(E(-d)=2\), and the author slightly strengthens the sufficient conditions that there be no such \(d\). It is also shown that \(E(-d)=3\) only finitely often. Finally, if there is a neighborhood of one which contains no zero of any zeta function of any complex quadratic field, then \(E(-d)\gg (\log d)^{1/2-\varepsilon}\).
Reviewer: P. J. Weinberger


11R11 Quadratic extensions
11R29 Class numbers, class groups, discriminants
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