A bound for the 3-part of class numbers of quadratic fields by means of the square sieve

Journal Article

We prove a nontrivial bound of O(D27/56+ε) for the 3-part of the class number of a quadratic field (√D) by using a variant of the square sieve and the q-analogue of van der Corput's method to count the number of squares of the form 4x3 - dz2 for a square-free positive integer d and bounded x, z. © de Gruyter 2006.