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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 18, Issue 4

Issues

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

Lillian B Pierce
Published Online: 2006-08-14 | DOI: https://doi.org/10.1515/FORUM.2006.034

Abstract

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 3dz 2 for a square-free positive integer d and bounded x, z.

About the article


Received: 2004-07-19

Published Online: 2006-08-14

Published in Print: 2006-07-01


Citation Information: Forum Mathematicum, Volume 18, Issue 4, Pages 677–698, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/FORUM.2006.034.

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Citing Articles

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[1]
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Research in Number Theory, 2018, Volume 4, Number 3
[2]
S. Holmin, N. Jones, P. Kurlberg, C. McLeman, and K. Petersen
Experimental Mathematics, 2017, Page 1
[3]
Martin Widmer
Bulletin of the London Mathematical Society, 2017
[4]
Jordan Ellenberg, Lillian Pierce, and Melanie Wood
Algebra & Number Theory, 2017, Volume 11, Number 8, Page 1739
[5]
D.R. Heath-Brown and Lillian B. Pierce
Journal of Number Theory, 2012, Volume 132, Number 8, Page 1741
[6]
D. R Heath-Brown
Forum Mathematicum, 2008, Volume 20, Number 2

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