| Title:
|
On the distribution of the roots of polynomial $z^k-z^{k-1}-\dots - z-1$ (English) |
| Author:
|
Gómez, Carlos A. |
| Author:
|
Luca, Florian |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
62 |
| Issue:
|
3 |
| Year:
|
2021 |
| Pages:
|
291-296 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the polynomial $f_k(z) = z^k-z^{k-1}-\cdots -z-1$ for $k\ge 2$ which arises as the characteristic polynomial of the $k$-generalized Fibonacci sequence. In this short paper, we give estimates for the absolute values of the roots of $f_k(z)$ which lie inside the unit disk. (English) |
| Keyword:
|
polynomial root distribution |
| MSC:
|
11B39 |
| MSC:
|
12F10 |
| idMR:
|
MR4331283 |
| DOI:
|
10.14712/1213-7243.2021.025 |
| . |
| Date available:
|
2021-10-18T08:29:39Z |
| Last updated:
|
2023-10-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149145 |
| . |
| Reference:
|
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| Reference:
|
[2] Everest G., van der Poorten A., Shparlinski I., Ward T.: Recurrence Sequences.Mathematical Surveys and Monographs, 104, American Mathematical Society, Providence, 2003. 10.1090/surv/104/06 |
| Reference:
|
[3] Gómez C. A., Luca F.: On the zero-multiplicity unitary of a fifth-order linear recurrences.International Journal of Number Theory 15 (2018), no. 3, 585–595. |
| Reference:
|
[4] Hua L. K., Wang Y.: Applications of Number Theory to Numerical Analysis.Springer, Berlin, 1981. Zbl 0465.10045 |
| Reference:
|
[5] Marques D., Trojovský P.: On characteristic polynomial of higher order generalized Jacobsthal numbers.Adv. Difference Equ. 2019 (2019), Paper No. 392, 9 pages. |
| Reference:
|
[6] Miles E. P., Jr.: Generalized Fibonacci numbers and associated matrices.Amer. Math. Monthly 67 (1960), 745–752. 10.1080/00029890.1960.11989593 |
| Reference:
|
[7] Miller M. D.: Mathematical notes: On generalized Fibonacci numbers.Amer. Math. Monthly 78 (1971), no. 10, 1108–1109. |
| Reference:
|
[8] Soundararajan K.: Equidistribution of zeros of polynomials.Amer. Math. Monthly 126 (2019), no. 3, 226–236. 10.1080/00029890.2019.1546078 |
| Reference:
|
[9] Wolfram D. A.: Solving generalized Fibonacci recurrences.Fibonacci Quart. 36 (1998), no. 2, 129–145. |
| . |
