This article is cited in 1 paper

Algebraic number fields with large class number

V. G. Sprindzhuk


Abstract: We prove that “almost all” real quadratic fields of a given type have a large ideal class number. For example, the number of ideal classes of the fields $\mathbf Q\bigl(\sqrt{m(m+1)(m+2)(m+3)}\,\bigr)$, where $\mathbf Q$ is the field of rational numbers, grows unbounded with $m$, as $m$ ranges through all natural numbers, except for a very sparse sequence. An analogous fact is established for the fields of Ankeny–Brauer–Chowla [5].

UDC: 511

MSC: Primary 12A50, 12A25; Secondary 12A35

Received: 28.11.1972

 English version: Mathematics of the USSR-Izvestiya, 1974, 8:5, 967–978

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