Extreme values of class numbers of real quadratic fields

Original · EN

We improve a result of H. L. Montgomery and J. P. Weinberger by establishing the existence of infinitely many fundamental discriminants d>0 for which the class number of the real quadratic field Q(√d) exeeds (2eγ+o(1)) √d(d)/ d. We believe this bound to be best possible. We also obtain upper and lower bounds of nearly the same order of magnitude, for the number of real quadratic fields with discriminant d≤ x which have such an extreme class number.