zbMATH — the first resource for mathematics

On the difference of the Weil height and the Neron-Tate height. (English) Zbl 0303.14003

14G99 Arithmetic problems in algebraic geometry; Diophantine geometry
14G05 Rational points
Full Text: DOI EuDML
[1] Cassels, J.W.S.: Diophantine equations with special reference to elliptic curves. J. London Math. Soc.41, 193-291 (1966) · Zbl 0138.27002
[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)
[3] Dem’janenko, V.A.: Estimate of the remainder term in Tate’s formula. Mat. Zametki3, 271-278 (1968)?Math. Notes3, 173-177 (1968)
[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)
[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)
[6] Dem’janenko, V.A.: On Tate height. Doklady Akad. Nauk SSSR212, 1043-1045 (1973)?Soviet Math., Doklady14, 1512-1515 (1973)
[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)
[8] Hasse, H.: Zahlentheorie. Berlin: Akademie-Verlag 1963
[9] Lang, S.: Diophantine Geometry. New York: Interscience 1962 · Zbl 0115.38701
[10] Lang, S.: Les formes bilinéaires de Néron et Tate. In: Séminaire Bourbaki no.274, mai 1964. Paris: Secrétariat mathématique 1964
[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) · Zbl 0072.03202
[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)
[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)
[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)
[15] Néron, A.: Quasi-fonctions et hauteurs sur les variétés abéliennes. Ann. of Math., II. Ser.82, 249-331 (1965) · Zbl 0163.15205
[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
[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) · Zbl 0256.14018
[18] Zimmer, H.G.: Die Néron-Tate’schen quadratischen Formen auf der rationalen Punktgruppe einer elliptischen Kurve. J. Number Theory2, 459-499 (1970) · Zbl 0204.21402
[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) · Zbl 0187.30802
[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) · Zbl 0305.14006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.