Geodesic
On the negative Pell equation
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 53-62 
E. P. Golubeva. On the negative Pell equation. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 53-62. http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a2/
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     author = {E. P. Golubeva},
     title = {On the negative {Pell} equation},
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     year = {2010},
     volume = {383},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a2/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $\varepsilon$ be the fundamental unit of a field $Q(\sqrt d)$. In the paper it is proved that $\varepsilon>d^{3/2}/\log^2d$ for almost all $d$ such that $N(\varepsilon)=-1$. Bibl. 6 titles.

[1] W. Narkiewicz, Elementary and analytic theory of algebraic numbers, Warszawa, 1974 | MR | Zbl

[2] V. Blomer, On the negative Pell equation, Preprint, 2006

[3] E. Fouvry, J. Küners, “On the negative Pell equation”, Annals of Mathematics (to appear)

[4] C. Hooley, “On the Pellian equation an the class number of indefinite binary quadratic forms”, J. reine und angew. Math., 353 (1984), 98–131 | DOI | MR | Zbl

[5] E. P. Golubeva, “O chislakh klassov veschestvennykh kvadratichnykh polei diskriminanta $4p$”, Zap. nauchn. semin. POMI, 204, 1993, 11–36 | MR | Zbl

[6] B. A. Venkov, Elementarnaya teoriya chisel, M.–L., 1937 | Zbl