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Izv. Akad. Nauk SSSR Ser. Mat., 1974, Volume 38, Issue 5, Pages 971–982 (Mi izv1997)  

This article is cited in 1 scientific paper (total in 1 paper)

Algebraic number fields with large class number

V. G. Sprindzhuk


Abstract: We prove that “almost all” real quadratic fields of a given type have a large ideal class number. For example, the number of ideal classes of the fields $\mathbf Q(\sqrt{m(m+1)(m+2)(m+3)} )$, where $\mathbf Q$ is the field of rational numbers, grows unbounded with $m$, as $m$ ranges through all natural numbers, except for a very sparse sequence. An analogous fact is established for the fields of Ankeny–Brauer–Chowla [5].

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English version:
Mathematics of the USSR-Izvestiya, 1974, 8:5, 967–978

Bibliographic databases:

UDC: 511
MSC: Primary 12A50, 12A25; Secondary 12A35
Received: 28.11.1972

Citation: V. G. Sprindzhuk, “Algebraic number fields with large class number”, Izv. Akad. Nauk SSSR Ser. Mat., 38:5 (1974), 971–982; Math. USSR-Izv., 8:5 (1974), 967–978

Citation in format AMSBIB
\Bibitem{Spr74}
\by V.~G.~Sprindzhuk
\paper Algebraic number fields with large class number
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1974
\vol 38
\issue 5
\pages 971--982
\mathnet{http://mi.mathnet.ru/izv1997}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=357374}
\zmath{https://zbmath.org/?q=an:0321.12007}
\transl
\jour Math. USSR-Izv.
\yr 1974
\vol 8
\issue 5
\pages 967--978
\crossref{https://doi.org/10.1070/IM1974v008n05ABEH002134}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. G. Sprindzhuk, “Achievements and problems in Diophantine approximation theory”, Russian Math. Surveys, 35:4 (1980), 1–80  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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