On the multiplicity of linear recurrence sequences
β Scribed by Patrick B. Allen
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 96 KB
- Volume
- 126
- Category
- Article
- ISSN
- 0022-314X
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β¦ Synopsis
We prove a lemma regarding the linear independence of certain vectors and use it to improve on a bound due to Schmidt on the zero-multiplicity of linear recurrence sequences.
π SIMILAR VOLUMES
Let F (z) β R[z] be a polynomial with positive leading coefficient, and let Ξ± > 1 be an algebraic number. For r = deg F > 0, assuming that at least one coefficient of F lies outside the field Q(Ξ±) if Ξ± is a Pisot number, we prove that the difference between the largest and the smallest limit points
In this paper we investigate linear three-term recurrence formulae with sequences of integers (T (n)) n 0 and (U (n)) n 0 , which are ultimately periodic modulo m, e.g. (T (n) mod m) n 0 = (a 0 , a 1 , a 2 , .
We prove some stability results for linear recurrences with constant coefficients in normed spaces. As a consequence we obtain a complete solution of the problem of the Hyers-Ulam stability for such recurrences.