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Zap. Nauchn. Sem. LOMI, 1979, Volume 82, Pages 5–28 (Mi znsl2090)  

Orders of the torsion of points of curves of genus 1

V. A. Dem'yanenko


Abstract: Let $K$ be an algebraic number field of degree $n$; $h(K)$ let be the number of divisor classes of the field $K$; $Y:v^2=u^4+au^2+b$ is the Jacobian curve over $K$; $b(a^2-4b)=c^2\prod^N_{i=1}q_i$ where $C$ is an integral divisor, $q_1,…,q_N$ are distinct prime divisors. One proves that there exists an effectively computable constant $c=c(n,h(K),N)$, such that the order $m$ of the torsion of any primitive $K$-point on $Y$ is bounded by it: $m\leqslant c$.

Full text: PDF file (1378 kB)

English version:
Journal of Soviet Mathematics, 1982, 18:6, 843–861

Bibliographic databases:

UDC: 511.51

Citation: V. A. Dem'yanenko, “Orders of the torsion of points of curves of genus 1”, Studies in number theory. Part 5, Zap. Nauchn. Sem. LOMI, 82, "Nauka", Leningrad. Otdel., Leningrad, 1979, 5–28; J. Soviet Math., 18:6 (1982), 843–861

Citation in format AMSBIB
\Bibitem{Dem79}
\by V.~A.~Dem'yanenko
\paper Orders of the torsion of points of curves of genus~1
\inbook Studies in number theory. Part~5
\serial Zap. Nauchn. Sem. LOMI
\yr 1979
\vol 82
\pages 5--28
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl2090}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=537020}
\zmath{https://zbmath.org/?q=an:0479.14016|0449.14004}
\transl
\jour J. Soviet Math.
\yr 1982
\vol 18
\issue 6
\pages 843--861
\crossref{https://doi.org/10.1007/BF01763959}


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