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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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$S$-integral points of $\mathbb {P}^n-\{2n+1$ hyperplanes in general position over number fields and function fields}
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by Julie T.-Y. Wang PDF
Trans. Amer. Math. Soc. 348 (1996), 3379-3389 Request permission

Abstract:

For the number field case we will give an upper bound on the number of the $S$-integral points in $\mathbb {P}^n(K)-\{ 2n+1\text { hyperplanes in general}$ $\text {position}\}$. The main tool here is the explicit upper bound of the number of solutions of $S$-unit equations (Invent. Math. 102 (1990), 95–107). For the function field case we will give a bound on the height of the $S$-integral points in $\mathbb {P}^n(K)-\{ 2n+1\text { hyperplanes in general position}\}$. We will also give a bound for the number of β€œgenerators" of those $S$-integral points. The main tool here is the $S$-unit Theorem by Brownawell and Masser (Proc. Cambridge Philos. Soc. 100 (1986), 427–434).
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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
  • MR Author ID: 364623
  • ORCID: 0000-0003-2133-1178
  • Received by editor(s): November 7, 1994
  • Received by editor(s) in revised form: July 10, 1995
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 3379-3389
  • MSC (1991): Primary 14G05; Secondary 11R58
  • DOI: https://doi.org/10.1090/S0002-9947-96-01568-1
  • MathSciNet review: 1340189