The Journal of the Indian Mathematical Society

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Numerical Investigations Related to the L-Series of Certain Elliptic Curves


Affiliations
1 Max-Planck-Institut fur Mathematik, Gottfried-Claren-Strasse 26 5300 Bonn F.R.G., Germany
2 Loewe Opta, 8640 Kronach, Germany
     

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According to the theorem of Mordell, the set of rational solutions E(Q) of an elliptic curve E over the rational numbers is a finitely generated abelian group. The rank of this group is called the rank of the elliptic curve and is the basic invariant of E; it is positive if and only if the equation defining E has infinitely many rational solutions.
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  • Numerical Investigations Related to the L-Series of Certain Elliptic Curves

Abstract Views: 213  |  PDF Views: 0

Authors

D. Zagier
Max-Planck-Institut fur Mathematik, Gottfried-Claren-Strasse 26 5300 Bonn F.R.G., Germany
G. Kramarz
Loewe Opta, 8640 Kronach, Germany

Abstract


According to the theorem of Mordell, the set of rational solutions E(Q) of an elliptic curve E over the rational numbers is a finitely generated abelian group. The rank of this group is called the rank of the elliptic curve and is the basic invariant of E; it is positive if and only if the equation defining E has infinitely many rational solutions.