Primitive points on elliptic curves

Rajiv Gupta; M. Ram Murty

Compositio Mathematica (1986)

  • Volume: 58, Issue: 1, page 13-44
  • ISSN: 0010-437X

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Gupta, Rajiv, and Ram Murty, M.. "Primitive points on elliptic curves." Compositio Mathematica 58.1 (1986): 13-44. <http://eudml.org/doc/89763>.

@article{Gupta1986,
author = {Gupta, Rajiv, Ram Murty, M.},
journal = {Compositio Mathematica},
keywords = {elliptic analogue of Artin's conjecture; primitive roots; complex multiplication},
language = {eng},
number = {1},
pages = {13-44},
publisher = {Martinus Nijhoff Publishers},
title = {Primitive points on elliptic curves},
url = {http://eudml.org/doc/89763},
volume = {58},
year = {1986},
}

TY - JOUR
AU - Gupta, Rajiv
AU - Ram Murty, M.
TI - Primitive points on elliptic curves
JO - Compositio Mathematica
PY - 1986
PB - Martinus Nijhoff Publishers
VL - 58
IS - 1
SP - 13
EP - 44
LA - eng
KW - elliptic analogue of Artin's conjecture; primitive roots; complex multiplication
UR - http://eudml.org/doc/89763
ER -

References

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  1. [1] E. Bombieri: Le grand crible dans la théorie analytique des nombres. Société mathematique de France. Asterisque18 (1974). Zbl0292.10035MR371840
  2. [2] J. Coates and A. Wiles: On the conjecture of Birch and Swinnerton-Dyer, Inv. Math.39 (1977) 223-251. Zbl0359.14009MR463176
  3. [3] E. Fouvry and H. Iwaniec: Primes in arithmetic progressions. Acta Arithmetica42 (1983) 197-218. Zbl0517.10045MR719249
  4. [4] R. Gupta: Fields of division points of elliptic curves related to Coates-Wiles, Ph.D. Thesis, M.I.T. (1983). 
  5. [5] R. Gupta and M. Ram Murty: A remark on Artin's conjectureInv. Math.78 (1984) 127-130. Zbl0549.10037MR762358
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  7. [7] C. Hooley: Applications of sieve Methods to the Theory of Numbers. Cambridge Univ. Press, London (1976). Zbl0327.10044MR404173
  8. [8] M. Huxley: The large sieve inequality for algebraic number fields III, Zero density results. J. London Math. Soc.3 (1971) 233-240. Zbl0213.07101MR276196
  9. [9] H. Iwaniec: Rosser's sieve. Acta Arith.36 (1980) 171-202. Zbl0435.10029MR581917
  10. [10] J. Lagarias and A. Odlyzko: Effective versions of the Cebotarev density theorem. In: A. Frolich (ed.), Algebraic Number Fields. Proceedings of the 1975 Durham Symposium, Academic Press, London and New York (1977). Zbl0362.12011MR447191
  11. [11] S. Lang: Elliptic Curves and diophantine Analysis. Springer-Verlag (1978). Zbl0388.10001MR518817
  12. [12] S. Lang and H. Trotter: Primitive points on elliptic curves. Bull. Amer. Math. Soc.83 (1977) 289-292. Zbl0345.12008MR427273
  13. [13] M. Ram Murty: On Artin's conjecture. J. Number Theory16 (1983) 147-168. Zbl0526.12010
  14. [14] K. Ribet: Dividing rational points on abelian varieties of CM type. Comp. Math.33 (1976) 69-74. Zbl0331.14020MR424823
  15. [15] J.P. Serre: Quelques applications du théorème de densité de Chebotarev. Publ. Math. I.H.E.S. 54 (1982) 123-201. Zbl0496.12011MR644559
  16. [16] W. Schaal: On the large sieve method in algebraic number fields. J. Number Theory2 (1970) 249-270. Zbl0198.07101MR272745
  17. [17] A. Walfisz: Über Gitterpunkte in mehrdimensionalen Ellipsoiden III. Akh. Math. Zietschr.27 (1978) S. 245-268. Zbl53.0158.02MR1544910JFM53.0158.02

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