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Zapiski Nauchnykh Seminarov POMI, 1993, Volume 204, Pages 11–36 (Mi znsl5781)  

This article is cited in 4 scientific papers (total in 4 papers)

The class numbers of real quadratic fields of discriminant $4p$

E. P. Golubeva
Full-text PDF (938 kB) Citations (4)
Abstract: For $p$ prime, $p=3\,(\operatorname{mod}4)$, we study the expansion of $\sqrt p$ into a continued fraction. In particular, we show that in the expansion
$$ \sqrt p=[n,\overline{l_1,\dots,l_L,l,l_L,\dots,l_1,2n}] $$
$l_1,\dots,l_L$ satisfy at least $L/2$ linear relations. We also obtain a new lower bound for the fundamental unit $\varepsilon_p$ of the field $\mathbb Q(\sqrt p)$ for almost all $p$ under consideration: $\varepsilon_p>p^3/\log^{1+\delta}p$ for all $p\ge x$ with $O(x/\log^{1+\delta}x)$ possible exceptions (here $\delta>0$ is an arbitrary constant), and an estimate for the mean value of the class number of $\mathbb Q(\sqrt p)$ with respect to averaging over $\varepsilon_p$:
$$ \sum_{p\equiv3\,(\operatorname{mod}4),\ \varepsilon_p\le x}h(p)=O(x). $$
Bibliography: 11 titles.
English version:
Journal of Mathematical Sciences, 1996, Volume 79, Issue 5, Pages 1277–1292
DOI: https://doi.org/10.1007/BF02366457
Bibliographic databases:
Document Type: Article
UDC: 511.622
Language: Russian
Citation: E. P. Golubeva, “The class numbers of real quadratic fields of discriminant $4p$”, Analytical theory of numbers and theory of functions. Part 11, Zap. Nauchn. Sem. POMI, 204, Nauka, St. Petersburg, 1993, 11–36; J. Math. Sci., 79:5 (1996), 1277–1292
Citation in format AMSBIB
\Bibitem{Gol93}
\by E.~P.~Golubeva
\paper The class numbers of real quadratic fields of discriminant~$4p$
\inbook Analytical theory of numbers and theory of functions. Part~11
\serial Zap. Nauchn. Sem. POMI
\yr 1993
\vol 204
\pages 11--36
\publ Nauka
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5781}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1216864}
\zmath{https://zbmath.org/?q=an:0814.11023|0844.11027}
\transl
\jour J. Math. Sci.
\yr 1996
\vol 79
\issue 5
\pages 1277--1292
\crossref{https://doi.org/10.1007/BF02366457}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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