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ON THE GROWTH OF LINEAR RECURRENCES IN FUNCTION FIELDS
Published online by Cambridge University Press: 09 November 2020
Abstract
Let
$ (G_n)_{n=0}^{\infty } $
be a nondegenerate linear recurrence sequence whose power sum representation is given by
$ G_n = a_1(n) \alpha _1^n + \cdots + a_t(n) \alpha _t^n $
. We prove a function field analogue of the well-known result in the number field case that, under some nonrestrictive conditions,
$ |{G_n}| \geq ( \max _{j=1,\ldots ,t} |{\alpha _j}| )^{n(1-\varepsilon )} $
for
$ n $
large enough.
MSC classification
- Type
- Research Article
- Information
- Creative Commons
- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Copyright
- © 2020 Australian Mathematical Publishing Association Inc.
Footnotes
Supported by Austrian Science Fund (FWF): I4406.
References
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