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Mat. Sb. (N.S.), 1973, Volume 90(132), Number 2, Pages 320–324 (Mi msb3020)  

This article is cited in 9 scientific papers (total in 9 papers)

Elliptic curves of infinite rank over $\Gamma$-extensions

P. F. Kurchanov


Abstract: In this paper we construct examples of elliptic curves over $\Gamma$-extensions of a specific class of fields.
Bibliography: 9 titles.

Full text (in Russian): PDF file (520 kB)
References (in Russian): PDF file   HTML файл

English version:
Mathematics of the USSR-Sbornik, 1973, 19:2, 320–324

Bibliographic databases:

UDC: 511.6
MSC: Primary 14H45; Secondary 14K22
Received: 20.05.1972

Citation: P. F. Kurchanov, “Elliptic curves of infinite rank over $\Gamma$-extensions”, Mat. Sb. (N.S.), 90(132):2 (1973), 320–324

Citation in format AMSBIB
\Bibitem{Kur73}
\by P.~F.~Kurchanov
\paper Elliptic curves of infinite rank over $\Gamma$-extensions
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 90(132)
\issue 2
\pages 320--324
\mathnet{http://mi.mathnet.ru/msb3020}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=327775}
\zmath{http://zbmath.org/?q=an:0252.14008}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 19
\issue 2
\pages 320--324
\crossref{http://dx.doi.org/10.1070/SM1973v019n02ABEH001762}


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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. П. Ф. Курчанов, “О ранге эллиптических кривых над $\Gamma$-расширениями”, Матем. сб., 93(135):3 (1974), 460–466  mathnet  mathscinet  zmath; P. F. Kurchanov, “On the rank of elliptic curves over $\Gamma$-extensions”, Math. USSR-Sb., 22:3 (1974), 465–472  crossref
    2. В. Г. Беркович, “О делении на изогению точек эллиптической кривой”, Матем. сб., 93(135):3 (1974), 467–486  mathnet  mathscinet  zmath; V. G. Berkovich, “On the division by an isogeny of the points of an elliptic curve”, Math. USSR-Sb., 22:3 (1974), 473–492  crossref
    3. П. Ф. Курчанов, “Дзета-функция эллиптических кривых над некоторыми абелевыми расширениями мнимых квадратичных полей”, Матем. сб., 102(144):1 (1977), 56–70  mathnet  mathscinet  zmath; P. F. Kurchanov, “The zeta-function of elliptic curves over certain Abelian extensions of imaginary quadratic fields”, Math. USSR-Sb., 31:1 (1977), 49–62  crossref
    4. Wulf-Dieter Geyer, Moshe Jarden, “Torsion points of elliptic curves over large algebraic extensions of finitely generated fields”, Isr J Math, 31:3-4 (1978), 257  crossref  mathscinet  zmath
    5. Michael Harris, “Systematic growth of Mordell-Weil groups of abelian varieties in towers of number fields”, Invent math, 51:2 (1979), 123  crossref  mathscinet  zmath
    6. David E. Rohrlich, “OnL-functions of elliptic curves and anticyclotomic towers”, Invent math, 75:3 (1984), 383  crossref  mathscinet  zmath
    7. Ю. Г. Зархин, “Кручение и эндоморфизмы абелевых многообразий над бесконечными расширениями числовых полей”, Изв. АН СССР. Сер. матем., 55:3 (1991), 658–669  mathnet  mathscinet  zmath  adsnasa; Yu. G. Zarhin, “Torsion and endomorphisms of Abelian varieties over infinite extensions of number fields”, Math. USSR-Izv., 38:3 (1992), 647–657  crossref
    8. Michael Rosen, Siman Wong, “The Rank of Abelian Varieties over Infinite Galois Extensions”, Journal of Number Theory, 92:1 (2002), 182  crossref
    9. И. С. Рахимов, “О поведении арифметических инвариантов некоторого класса эллиптических кривых в круговых $\Gamma$-расширениях”, Матем. тр., 8:1 (2005), 122–134  mathnet  mathscinet  zmath  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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