Abstract
Let \(\mathcal {F}(h)\) be the number of imaginary quadratic fields with class number h. In this note, we improve the error term in Soundararajan’s asymptotic formula for the average of \(\mathcal {F}(h)\). Our argument leads to a similar refinement of the asymptotic for the average of \(\mathcal {F}(h)\) over odd h, which was recently obtained by Holmin, Jones, Kurlberg, McLeman and Petersen.
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The author is partially supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada.
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Lamzouri, Y. On the average of the number of imaginary quadratic fields with a given class number. Ramanujan J 44, 411–416 (2017). https://doi.org/10.1007/s11139-017-9910-9
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DOI: https://doi.org/10.1007/s11139-017-9910-9