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BIRS Workshop Lecture Videos

Large values of class numbers of real quadratic fields Lamzouri, Youness


Improving a result of Montgomery and Weinberger, we establish the existence of infinitely many real quadratic fields for which the class numbers are as large as possible. These values are achieved using a special family of fields, first studied by Chowla. In a subsequent work, joint with A. Dahl, we investigate the distribution of class numbers in Chowla’s family, and show a strong similarity between this distribution and that of class numbers of imaginary quadratic fields. As an application of our results, we determine the average order of the number of real quadratic fields in Chowla’s family with class number \(h\).

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