Advertisement

Mathematische Zeitschrift

, Volume 147, Issue 1, pp 35–51 | Cite as

On the difference of the Weil height and the Néron-Tate height

  • Horst Günter Zimmer
Article

Keywords

Weil Height 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cassels, J.W.S.: Diophantine equations with special reference to elliptic curves. J. London Math. Soc.41, 193–291 (1966)Google Scholar
  2. 2.
    Dem'janenko, V.A.: Points of finite order on elliptic curves. Izvestija Akad. Nauk SSSR, Ser. Mat.31, 1327–1340 (1967)—Math. USSR, Izvestija1, 1271–1284 (1967)Google Scholar
  3. 3.
    Dem'janenko, V.A.: Estimate of the remainder term in Tate's formula. Mat. Zametki3, 271–278 (1968)—Math. Notes3, 173–177 (1968)Google Scholar
  4. 4.
    Dem'janenko, V.A.: On torsion points of elliptic curves. Izvestija Akad. Nauk SSSR, Ser. Mat.34, 757–774 (1970)—Math. USSR, Izvestija4, 765–783 (1970)Google Scholar
  5. 5.
    Dem'janenko, V.A.: Torsion of elliptic curves. Izvestija Akad. Nauk SSSR, Ser. Mat.35, 280–307 (1971)—Math. USSR, Izvestija5, 289–318 (1971)Google Scholar
  6. 6.
    Dem'janenko, V.A.: On Tate height. Doklady Akad. Nauk SSSR212, 1043–1045 (1973)—Soviet Math., Doklady14, 1512–1515 (1973)Google Scholar
  7. 7.
    Dem'janenko, V.A.: On the Tate height and the representation of numbers by binary forms. Izvestija Akad. Nauk SSSR, Ser. Mat.38, 459–470 (1974)—Math. USSR, Izvestija8, 463–476 (1974)Google Scholar
  8. 8.
    Hasse, H.: Zahlentheorie. Berlin: Akademie-Verlag 1963Google Scholar
  9. 9.
    Lang, S.: Diophantine Geometry. New York: Interscience 1962Google Scholar
  10. 10.
    Lang, S.: Les formes bilinéaires de Néron et Tate. In: Séminaire Bourbaki no.274, mai 1964. Paris: Secrétariat mathématique 1964Google Scholar
  11. 11.
    Manin, Ju. I.: On cubic congruences to a prime modulus. Izvestija Akad. Nauk SSSR, Ser. Mat.20, 673–678 (1956)—Amer. Math. Soc. Translat., II. Ser.13, 1–7 (1960)Google Scholar
  12. 12.
    Manin, Ju.I.: The Tate height on an Abelian variety. Its variants and applications. Izvestija Akad. Nauk SSSR, Ser. Mat.28, 1363–1390 (1964)—Amer. Math. Soc. Translat., II. Ser.59, 82–110 (1966)Google Scholar
  13. 13.
    Manin, Ju.I.: The refined structure of the Néron-Tate height. Mat. Sbornik, N. Ser.83 (125), 331–348 (1970)—Math. USSR, Sbornik12, 325–342 (1970)Google Scholar
  14. 14.
    Manin, Ju.I.: Cyclotomic fields and modular curves. Uspehi Mat. Nauk26, no. 6 (162), 7–71 (1971)—Russ. Math. Surveys26, no. 6, 7–78 (1971)Google Scholar
  15. 15.
    Néron, A.: Quasi-fonctions et hauteurs sur les variétés abéliennes. Ann. of Math., II. Ser.82, 249–331 (1965)Google Scholar
  16. 16.
    Néron, A.: Hauteurs et théorie des intersections. In: Centro Internazionale Matematico Estivo (C.I.M.E.): Questions on algebraic varieties. (III Ciclo, Varenna, 7–17 Settembre 1969.) pp. 101–120. Roma: Edizioni Cremonese 1970Google Scholar
  17. 17.
    Zarhin, Ju.G., and Manin, Ju.I.: Height on families of Abelian varieties. Mat. Sbornik, N. Ser.89 (131), 171–181 (1972)—Math. USSR, Sbornik18, 169–179 (1972)Google Scholar
  18. 18.
    Zimmer, H.G.: Die Néron-Tate'schen quadratischen Formen auf der rationalen Punktgruppe einer elliptischen Kurve. J. Number Theory2, 459–499 (1970)Google Scholar
  19. 19.
    Zimmer, H.G.: An elementary proof of the Riemann hypothesis for an elliptic curve over a finite field. Pacific J. Math.36, 267–278 (1971)Google Scholar
  20. 20.
    Zimmer, H.G.: Ein Analogon des Satzes von Nagell-Lutz über die Torsion einer elliptischen Kurve. J. reine angew. Math.268/269, 360–378 (1974)Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Horst Günter Zimmer
    • 1
  1. 1.Fachbereich 9 MathematikUniversität des SaarlandesSaarbrückenBundesrepublik Deutschland

Personalised recommendations