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

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References

  1. Cassels, J.W.S.: Diophantine equations with special reference to elliptic curves. J. London Math. Soc.41, 193–291 (1966)

    Google Scholar 

  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. 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. 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. 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. Dem'janenko, V.A.: On Tate height. Doklady Akad. Nauk SSSR212, 1043–1045 (1973)—Soviet Math., Doklady14, 1512–1515 (1973)

    Google Scholar 

  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. Hasse, H.: Zahlentheorie. Berlin: Akademie-Verlag 1963

    Google Scholar 

  9. Lang, S.: Diophantine Geometry. New York: Interscience 1962

    Google Scholar 

  10. Lang, S.: Les formes bilinéaires de Néron et Tate. In: Séminaire Bourbaki no.274, mai 1964. Paris: Secrétariat mathématique 1964

    Google Scholar 

  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. 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. 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. 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. Néron, A.: Quasi-fonctions et hauteurs sur les variétés abéliennes. Ann. of Math., II. Ser.82, 249–331 (1965)

    Google Scholar 

  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 1970

    Google Scholar 

  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. 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. 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. 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 

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Günter Zimmer, H. On the difference of the Weil height and the Néron-Tate height. Math Z 147, 35–51 (1976). https://doi.org/10.1007/BF01214273

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