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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 383, Pages 53–62 (Mi znsl3871)  
On the negative Pell equation

E. P. Golubeva

State University of Telecommunications, St. Petersburg, Russia
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Abstract: 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.
Key words and phrases: negative Pell equation, fundamental unit of a field, continued fraction.
Received: 27.10.2010
English version:
Journal of Mathematical Sciences (New York), 2011, Volume 178, Issue 2, Pages 144–149
DOI: https://doi.org/10.1007/s10958-011-0533-1
Bibliographic databases:
Document Type: Article
UDC: 511
Language: Russian
Citation: E. P. Golubeva, “On the negative Pell equation”, Analytical theory of numbers and theory of functions. Part 25, Zap. Nauchn. Sem. POMI, 383, POMI, St. Petersburg, 2010, 53–62; J. Math. Sci. (N. Y.), 178:2 (2011), 144–149
Citation in format AMSBIB
\Bibitem{Gol10}
\by E.~P.~Golubeva
\paper On the negative Pell equation
\inbook Analytical theory of numbers and theory of functions. Part~25
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 383
\pages 53--62
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3871}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 178
\issue 2
\pages 144--149
\crossref{https://doi.org/10.1007/s10958-011-0533-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80053481695}
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