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Lillian B Pierce

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 4x³ − dz² for a square-free positive integer d and bounded x, z.

Forum Mathematicum, Walter de Gruyter

Print ISSN: 0933-7741
Volume: 18, 07/2006
Pages: 677 - 698

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