---
_id: '34886'
abstract:
- lang: eng
  text: We give asymptotic upper and lower bounds for the number of squarefree d (0
    < d ≤ X) such that the equation x² − dy²= −1 is solvable. These estimates, as
    usual, can equivalently be interpreted in terms of real quadratic fields with
    a fundamental unit with norm −1 and give strong evidence in the direction of a
    conjecture due to P. Stevenhagen.
author:
- first_name: Étienne
  full_name: Fouvry, Étienne
  last_name: Fouvry
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Fouvry É, Klüners J. On the negative Pell equation. <i>Annals of Mathematics</i>.
    2010;172(3):2035-2104. doi:<a href="https://doi.org/10.4007/annals.2010.172.2035">10.4007/annals.2010.172.2035</a>
  apa: Fouvry, É., &#38; Klüners, J. (2010). On the negative Pell equation. <i>Annals
    of Mathematics</i>, <i>172</i>(3), 2035–2104. <a href="https://doi.org/10.4007/annals.2010.172.2035">https://doi.org/10.4007/annals.2010.172.2035</a>
  bibtex: '@article{Fouvry_Klüners_2010, title={On the negative Pell equation}, volume={172},
    DOI={<a href="https://doi.org/10.4007/annals.2010.172.2035">10.4007/annals.2010.172.2035</a>},
    number={3}, journal={Annals of Mathematics}, publisher={Annals of Mathematics},
    author={Fouvry, Étienne and Klüners, Jürgen}, year={2010}, pages={2035–2104} }'
  chicago: 'Fouvry, Étienne, and Jürgen Klüners. “On the Negative Pell Equation.”
    <i>Annals of Mathematics</i> 172, no. 3 (2010): 2035–2104. <a href="https://doi.org/10.4007/annals.2010.172.2035">https://doi.org/10.4007/annals.2010.172.2035</a>.'
  ieee: 'É. Fouvry and J. Klüners, “On the negative Pell equation,” <i>Annals of Mathematics</i>,
    vol. 172, no. 3, pp. 2035–2104, 2010, doi: <a href="https://doi.org/10.4007/annals.2010.172.2035">10.4007/annals.2010.172.2035</a>.'
  mla: Fouvry, Étienne, and Jürgen Klüners. “On the Negative Pell Equation.” <i>Annals
    of Mathematics</i>, vol. 172, no. 3, Annals of Mathematics, 2010, pp. 2035–104,
    doi:<a href="https://doi.org/10.4007/annals.2010.172.2035">10.4007/annals.2010.172.2035</a>.
  short: É. Fouvry, J. Klüners, Annals of Mathematics 172 (2010) 2035–2104.
date_created: 2022-12-23T09:09:02Z
date_updated: 2023-03-06T09:50:37Z
department:
- _id: '102'
doi: 10.4007/annals.2010.172.2035
intvolume: '       172'
issue: '3'
keyword:
- Statistics
- Probability and Uncertainty
- Mathematics (miscellaneous)
language:
- iso: eng
page: 2035-2104
publication: Annals of Mathematics
publication_identifier:
  issn:
  - 0003-486X
publication_status: published
publisher: Annals of Mathematics
status: public
title: On the negative Pell equation
type: journal_article
user_id: '93826'
volume: 172
year: '2010'
...