Weinberger, P. J. Exponents of class groups of complex quadratic fields. (English) Zbl 0217.04202 Acta Arith. 22, 117-124 (1973). 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 Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 26 Documents MSC: 11R11 Quadratic extensions 11R29 Class numbers, class groups, discriminants PDF BibTeX XML Cite \textit{P. J. Weinberger}, Acta Arith. 22, 117--124 (1973; Zbl 0217.04202) Full Text: DOI EuDML Online Encyclopedia of Integer Sequences: Euler’s ”numerus idoneus” (or ”numeri idonei”, or idoneal, or suitable, or convenient numbers). Discriminants of the known imaginary quadratic fields with 1 class per genus (a finite sequence). Discriminants of imaginary fields whose class group has exponent 2, negated. Odd terms in A003171: negated odd discriminants of orders of imaginary quadratic fields with 1 class per genus.