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A bound for the 3-part of class numbers of quadratic fields by means of the square sieve
We prove a nontrivial bound of O(|D|27/56+ε) for the 3-part of the class number of a quadratic field ℚ(√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 4x 3 − dz 2 for a square-free positive integer d and bounded x, z.
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