A Bound for the 3-part of Class Numbers of Quadratic Fields by Means of the Square Sieve
نویسنده
چکیده
We prove a nontrivial bound of O(|D|27/56+ ) 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.
منابع مشابه
The 3-Part of Class Numbers of Quadratic Fields
In 1801, Gauss published Disquisitiones Arithmeticae, which, among many other things, develops genus theory, describing the divisibility by 2 of class numbers of quadratic fields. In the centuries since this work, the divisibility properties of class numbers by integers g ≥ 3 have largely remained mysterious. In particular, the problem of bounding the g-part hg(D) of class numbers of quadratic ...
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