Counting points of small height on elliptic curves

 Access to full text

 Full (PDF)

1. [AM] ANDERSON (M.) and MASSER (D.W.). — Lower bounds for heights on elliptic curves, Math. Z., t. 174, 1980, p. 23-34. Zbl0421.14006MR82g:10049
2. [BM] BROWNAWELL (W.D.) and MASSER (D.W.). — Multiplicity estimates for analytic functions I, J. Reine Angew. Math., t. 314, 1979, p. 200-216. Zbl0417.10027MR81j:10046a
3. [C] COHEN (P.). — Explicit calculation of some effective constants in transcendence proofs, Ph. D. Thesis, University of Nottingham, 1985, Chapter 3. 
4. [Da] DAVID (S.). — Fonctions thêta et points de torsion des variétés abéliennes, C. R. Acad. Sci. Paris, t. 305, 1987, p. 211-214. Zbl0628.14035MR89b:11047
5. [Do] DOBROWOLSKI (E.). — On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arith., t. 34, 1979, p. 391-401. Zbl0416.12001MR80i:10040
6. [FP] FAISANT (A.) and PHILIBERT (G.). — Quelques résultats de transcendance liés à l'invariant modulaire j, J. Number Theory, t. 25, 1987, p. 184-200. Zbl0633.10035MR88f:11066
7. [H] HINDRY (M.). — Géométrie et hauteurs dans les groupes algébriques, Thèse de Doctorat de l'Université Paris VI, 1987. 
8. [I] IGUSA (J.). — Theta functions. — Berlin-Heidelberg-New York, Springer-Verlag, 1972. Zbl0251.14016MR48 #3972
9. [L] LAURENT (M.). — Minoration de la hauteur de Néron-Tate, [Séminaire de Théorie de Nombres, Paris 1981 — 2], Boston-Basel-Stuttgart, Birkhäuser, 1983, pp. 137-152. Zbl0521.14010MR85e:11048
10. [M] MASSER (D.W.). — Division fields of elliptic functions, Bull. London Math. Soc., t. 9, 1977, p. 49-53. Zbl0356.12018MR56 #2922
11. [M′] MASSER (D.W.). — Small values of heights on families of abelian varieties, [Lecture Notes in Math., vol. 1290], New York-Berlin-Heidelberg-Tokyo, Springer-Verlag, 1987, pp. 109-148. Zbl0639.14025MR89g:11048
12. [S] SILVERMAN (J.H.). — Lower bounds for the canonical height on elliptic curves, Duke Math. J., t. 48, 1981, p. 633-648. Zbl0475.14033MR82k:14043
13. [S′] SILVERMAN (J.H.). — The arithmetic of elliptic curves. — New York-Berlin-Heidelberg-Tokyo, Springer-Verlag, 1986. Zbl0585.14026MR87g:11070
14. [Z] ZIMMER (H.G.). — On the difference of the Weil height and the Néron-Tate height, Math. Z., t. 147, 1976, p. 35-51. Zbl0303.14003MR54 #7476
15. [Z′] ZIMMER (H.G.). — Quasi-functions on elliptic curves over number fields, J. Reine Angew. Math., t. 307, 1979, p. 221-246. Zbl0399.14014MR80g:14024

1. Evelina Viada, The intersection of a curve with algebraic subgroups in a product of elliptic curves
2. Sinnou David, Minorations de hauteurs sur les variétés abéliennes
3. Joseph H. Silverman, Lehmer’s conjecture for polynomials satisfying a congruence divisibility condition and an analogue for elliptic curves