|
Well-approximated points on linear extensions of elliptic curves
Author(s):
Deanna
M.
Caveny;
Robert
Tubbs
Journal:
Proc. Amer. Math. Soc.
138
(2010),
2745-2754.
MSC (2010):
Primary 11J89
Posted:
March 10, 2010
MathSciNet review:
2644889
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We employ a result on linear forms in logarithms of algebraic points on commutative algebraic groups, a study initiated by Philippon and Waldschmidt, a so-called ``local nullstellen inequality'' of Brownawell, and some elementary analytic estimates to study the approximation properties of coordinates of non-generic points on a linear (algebraic) group extension of an elliptic curve.
References:
-
- [Br]
- W. D. Brownawell, Local diophantine nullstellen inequalities, J. of the A.M.S. 1 (1988), No. 2, pp. 311-322. MR 928261 (89h:11041)
- [Ca-Tu]
- D. Caveny, R. Tubbs, The arithmetic of well-approximated numbers, in Number Theory with an Emphasis on the Markoff Spectrum, Pollington and Moran, eds., Marcel Dekker, New York, 1993, pp. 53-60. MR 1219324 (94b:11059)
- [Hi]
- M. Hindry, Groupes algébriques commutatifs, exemples explicites, Sem. d'Arithmétique Saint-Etienne, Université de Saint-Etienne, France, 1988-89, pp. 9-42.
- [H-K]
- N. Hirata-Kohno, Formes linéaires de logarithmes de points algébriques sur les groupes algébriques, Invent. Math. 104 (1991), pp. 401-433. MR 1098616 (91m:11050)
- [Ph-Wa]
- P. Philippon, M. Waldschmidt, Formes linéaires de logarithmes sur les groupes algébriques commutatifs, Ill. J. of Math. 32 (1988), No. 2, pp. 281-314. MR 945864 (89j:11070)
- [Re]
- E. Reyssat, Approximation algébrique de nombres liés aux fonctions elliptiques et exponentielle, Bull. Soc. Math. France 108 (1980), pp. 47-79. MR 603340 (82j:10064)
- [Se]
- J-P. Serre, Appendix in [Wa 1979]. MR 570648 (82k:10041)
- [Wa 2000]
- M. Waldschmidt, Diophantine Approximation on Linear Algebraic Groups, Springer, New York, 2000. MR 1756786 (2001c:11075)
- [Wa 1979]
- M. Waldschmidt, Nombres transcendants et groupes algébriques, Astérisque, 69-70, Sociéte Mathématiqué de France, 1979. MR 570648 (82k:10041)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2010):
11J89
Retrieve articles in all Journals with
MSC (2010):
11J89
Additional Information:
Deanna
M.
Caveny
Affiliation:
Department of Mathematics, College of Charleston, 66 George Street, Charleston, South Carolina 29424
Email:
cavenyd@cofc.edu
Robert
Tubbs
Affiliation:
Department of Mathematics, Campus Box 395, University of Colorado, Boulder, Colorado 80309
Email:
tubbs@euclid.colorado.edu
DOI:
10.1090/S0002-9939-10-10334-7
PII:
S 0002-9939(10)10334-7
Received by editor(s):
December 13, 2009
Posted:
March 10, 2010
Additional Notes:
The authors would like to thank the referee(s) for valuable and insightful feedback, which contributed to substantial improvements in the manuscript and its results.
Communicated by:
Wen-Ching Winnie Li
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
