Abstract
Let be an algebraically closed field of characteristic zero, let be a finitely generated subgroup of the multiplicative group of , and let be a quasiprojective variety defined over . We consider -valued sequences of the form , where and are rational maps defined over and is a point whose forward orbit avoids the indeterminacy loci of and . Many classical sequences from number theory and algebraic combinatorics fall under this dynamical framework, and we show that the set of for which is a finite union of arithmetic progressions along with a set of upper Banach density zero. In addition, we show that if for every and is irreducible and the orbit of is Zariski dense in then there is a multiplicative torus and maps and such that for some . We then obtain results about the coefficients of -finite power series using these facts.
Citation
Jason P. Bell. Shaoshi Chen. Ehsaan Hossain. "Rational dynamical systems, -units, and -finite power series." Algebra Number Theory 15 (7) 1699 - 1728, 2021. https://doi.org/10.2140/ant.2021.15.1699
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