{"page":"2035-2104","keyword":["Statistics","Probability and Uncertainty","Mathematics (miscellaneous)"],"publication_identifier":{"issn":["0003-486X"]},"year":"2010","_id":"34886","intvolume":" 172","language":[{"iso":"eng"}],"author":[{"last_name":"Fouvry","first_name":"Étienne","full_name":"Fouvry, Étienne"},{"last_name":"Klüners","full_name":"Klüners, Jürgen","first_name":"Jürgen","id":"21202"}],"date_updated":"2023-03-06T09:50:37Z","volume":172,"department":[{"_id":"102"}],"publication":"Annals of Mathematics","publication_status":"published","title":"On the negative Pell equation","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."}],"date_created":"2022-12-23T09:09:02Z","publisher":"Annals of Mathematics","user_id":"93826","citation":{"bibtex":"@article{Fouvry_Klüners_2010, title={On the negative Pell equation}, volume={172}, DOI={10.4007/annals.2010.172.2035}, 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.” *Annals of Mathematics* 172, no. 3 (2010): 2035–2104. https://doi.org/10.4007/annals.2010.172.2035.","ama":"Fouvry É, Klüners J. On the negative Pell equation. *Annals of Mathematics*. 2010;172(3):2035-2104. doi:10.4007/annals.2010.172.2035","apa":"Fouvry, É., & Klüners, J. (2010). On the negative Pell equation. *Annals of Mathematics*, *172*(3), 2035–2104. https://doi.org/10.4007/annals.2010.172.2035","ieee":"É. Fouvry and J. Klüners, “On the negative Pell equation,” *Annals of Mathematics*, vol. 172, no. 3, pp. 2035–2104, 2010, doi: 10.4007/annals.2010.172.2035.","mla":"Fouvry, Étienne, and Jürgen Klüners. “On the Negative Pell Equation.” *Annals of Mathematics*, vol. 172, no. 3, Annals of Mathematics, 2010, pp. 2035–104, doi:10.4007/annals.2010.172.2035.","short":"É. Fouvry, J. Klüners, Annals of Mathematics 172 (2010) 2035–2104."},"doi":"10.4007/annals.2010.172.2035","issue":"3","type":"journal_article","status":"public"}