Zeros of linear recurrence sequences
β Scribed by Hans Peter Schlickewei; Wolfgang M. Schmidt; Michel Waldschmidt
- Publisher
- Springer
- Year
- 1999
- Tongue
- English
- Weight
- 109 KB
- Volume
- 98
- Category
- Article
- ISSN
- 0025-2611
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We obtain asymptotic formulas for all the moments of certain arithmetic functions with linear recurrence sequences. We also apply our results to obtain asymptotic formulas for some mean values related to average orders of elements in finite fields.
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.
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