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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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Greatest common divisors with moving targets and consequences for linear recurrence sequences
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by Nathan Grieve and Julie Tzu-Yueh Wang PDF
Trans. Amer. Math. Soc. 373 (2020), 8095-8126 Request permission


We establish consequences of the moving form of Schmidt’s Subspace Theorem. Indeed, we obtain inequalities that bound the logarithmic greatest common divisor of moving multivariable polynomials evaluated at moving $S$-unit arguments. In doing so, we complement recent work of Levin. As an additional application, we obtain results that pertain to the greatest common divisor problem for algebraic linear recurrence sequences. These observations are motivated by previous related works of Corvaja-Zannier, Levin, and others.
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Additional Information
  • Nathan Grieve
  • Affiliation: The Tutte Institute for Mathematics and Computation, P.O. Box 9703, Terminal, Ottawa, Ontario, K1G 3Z4, Canada
  • MR Author ID: 1020249
  • ORCID: 0000-0003-3166-0039
  • Email:
  • Julie Tzu-Yueh Wang
  • Affiliation: Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan
  • MR Author ID: 364623
  • ORCID: 0000-0003-2133-1178
  • Email:
  • Received by editor(s): April 29, 2019
  • Received by editor(s) in revised form: August 27, 2019, and March 26, 2020
  • Published electronically: August 28, 2020
  • Additional Notes: The second author was supported in part by Taiwan’s MoST grant 108-2115-M-001-001-MY2.
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 8095-8126
  • MSC (2010): Primary 11J87; Secondary 11B37, 11J25
  • DOI:
  • MathSciNet review: 4169683