Greatest common divisors with moving targets and consequences for linear recurrence sequences

Grieve, Nathan; Wang, Julie

doi:10.1090/tran/8220

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

Abstract:

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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