On the 16-Rank of Class Groups of ℚ(√-2p) for Primes p ≡ 1 mod 4-Reference-Cited by-同舟云学术

On the 16-Rank of Class Groups of ℚ(√-2p) for Primes p ≡ 1 mod 4

Published:2018-02-05 Issue:23 Volume:2019 Page:7406-7427
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Koymans Peter¹,Milovic Djordjo²

Affiliation:

1. Mathematisch Instituut, Leiden University, CA Leiden, Netherlands

2. Department of Mathematics, University College London, Gower Street, London, UK

Abstract

Abstract We use Vinogradov’s method to prove equidistribution of a spin symbol governing the 16-rank of class groups of quadratic number fields $\mathbb{Q}(\sqrt{-2p})$, where p ≡ 1 mod 4 is a prime.

Funder

Division of Mathematical Sciences

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2019/23/7406/31146232/rny010.pdf

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3. “Is there a density for the set of primes p such that the class number of $\textbf{ Q}\left (\sqrt{-p}\right )$ is divisible by 16?” Topics in Classical Number Theory, Vol. I, II (Budapest, 1981).;Cohn,1984

4. Cohen-Lenstra heuristics of quadratic number fields.” In Algorithmic Number TheoryLecture Notes in Computer Science;Fouvry,2006

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