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On linear recurrence sequences with polynomial coefficients

Published online by Cambridge University Press:  18 May 2009

A. J. van der Poorten  and
I. E. Shparlinski
A. J. van der Poorten
Affiliation:
Centre for Number Theory Research, School of Mathematics, Physics, Computing and Electronics, Macquarie UniversityNSW 2109, Australia
I. E. Shparlinski
Affiliation:
Centre for Number Theory Research, School of Mathematics, Physics, Computing and Electronics, Macquarie UniversityNSW 2109, Australia
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We consider sequences (Ah)defined over the field ℚ of rational numbers and satisfying a linear homogeneous recurrence relation

with polynomial coefficients sj;. We shall assume without loss of generality, as we may, that the sj, are defined over ℤ and the initial values A0A]…, An−1 are integer numbers. Also, without loss of generality we may assume that S0 and Sn have no non-negative integer zero. Indeed, any other case can be reduced to this one by making a shift h → h – l – 1 where l is an upper bound for zeros of the corresponding polynomials (and which can be effectively estimated in terms of their heights)

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 2 , May 1996 , pp. 147 - 155
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

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