Abstract
We prove that almost real quadratic fields of a given type have a large ideal class number. For example, the number of ideal classes of the fields , where is the field of rational numbers, grows unbounded with , as ranges through all natural numbers, except for a very sparse sequence. An analogous fact is established for the fields of Ankeny-Brauer-Chowla, Amer. J. Math. 78 (1965), 51-61.
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