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 -integral points of  over number fields and function fields
Author(s):
Julie
T.-Y.
Wang
Journal:
Trans. Amer. Math. Soc.
348
(1996),
3379-3389.
MSC (1991):
Primary 14G05;
Secondary 11R58
MathSciNet review:
1340189
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Abstract:
For the number field case we will give an upper bound on the number of the  -integral points in 
 . The main tool here is the explicit upper bound of the number of solutions of  -unit equations (Invent. Math. 102 (1990), 95--107). For the function field case we will give a bound on the height of the  -integral points in  . We will also give a bound for the number of ``generators" of those  -integral points. The main tool here is the  -unit Theorem by Brownawell and Masser (Proc. Cambridge Philos. Soc. 100 (1986), 427--434).
References:
- [B-M]
- Brownawell, W.D. and Masser, D.W., Vanishing Sums in Function Fields, Math. Proc. Cambridge. Phil. Soc. 100 (1986), 427-434. MR 87k:11080
- [La 1]
- Lang, S., Fundamentals of Diophantine Geometry, Springer-Verlag, 1983. MR 85j:11005
- [La 2]
- Lang, S., Algebra, Addison-Wesley, 1984. MR 86j:00003
- [Ma]
- Mason, R.C., Diophantine Equations over Function Fields, LMS Lecture Notes 96, Cambrige Univ. Press, 1984. MR 86b:11026
- [R-W]
- Ru, M. and Wong, P.-M., Integral Points of
 , Invent. Math. 106 (1990), 195-216. MR 93f:11056 - [Schl]
- Schlickewei, H.P.,
 -unit Equations over Number Fields, Invent. Math. 102 (1990), 95-107. MR 92c:11028 - [Schm]
- Schmidt, W.M., Lecture Notes on Diophantine Approximation, University of Colorado, Boulder, 1989.
- [Vo]
- Vojta, P., Diophantine Approximations and Value Distribution Theory, Lecture Notes in Math., vol. 1239, Springer, Berlin, Heidelberg, New York, 1987. MR 91k:11049
- [Wa]
- Wang, J. T.-Y., The Truncated Second Main Theorem of Function Fields, J. Number Theory (to appear).
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Additional Information:
Julie
T.-Y.
Wang
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Address at time of publication:
Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
DOI:
10.1090/S0002-9947-96-01568-1
PII:
S 0002-9947(96)01568-1
Keywords:
$S$-integral points of $\mathbb{P}^n(K)-\{ 2n+1\text{ hyperplanes in general position}\}$
Received by editor(s):
November 7, 1994
Received by editor(s) in revised form:
July 10, 1995
Copyright of article:
Copyright
1996,
American Mathematical Society
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