On the negative Pell equation
É. Fouvry, J. Klüners, Annals of Mathematics 172 (2010) 2035–2104.
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Author
Fouvry, Étienne;
Klüners, JürgenLibreCat
Department
Abstract
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.
Publishing Year
Journal Title
Annals of Mathematics
Volume
172
Issue
3
Page
2035-2104
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Fouvry É, Klüners J. On the negative Pell equation. Annals of Mathematics. 2010;172(3):2035-2104. doi:10.4007/annals.2010.172.2035
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
@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} }
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.
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.
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.
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