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ON THE GROWTH OF LINEAR RECURRENCES IN FUNCTION FIELDS

Published online by Cambridge University Press:  09 November 2020

CLEMENS FUCHS
Affiliation:
Department of Mathematics, University of Salzburg, Hellbrunnerstr. 34, A-5020 Salzburg, Austria
SEBASTIAN HEINTZE
Affiliation:
Department of Mathematics, University of Salzburg, Hellbrunnerstr. 34, A-5020 Salzburg, Austria e-mail: sebastian.heintze@sbg.ac.at
Corresponding
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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.

Type
Research Article
Creative Commons
Creative Common License - CCCreative Common License - BY
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.

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