Inequalities For The Growth Of Rational Functions With Prescribed Poles
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915804104097792 |
|---|---|
| author | Rather, N. A. Wani, Mohmmad Shafi Bhat, Danish Rashid |
| author_facet | Rather, N. A. Wani, Mohmmad Shafi Bhat, Danish Rashid |
| contents | Let $\mathcal R_{n}$ be the set of all rational functions of the type $r(z) = f(z)/w(z)$, where $f(z)$ is a polynomial of degree at most $n$ and $w(z) = \prod_{j=1}^{n}(z-β_j)$, $|β_j|>1$ for $1\leq j\leq n$. In this work, we investigate the growth behavior of rational functions with prescribed poles by utilizing certain coefficients of the polynomial $f(z)$. The results obtained here not only refine and strengthen the findings of Rather et al. \cite{NS}, but also generalize recent growth estimates for polynomials due to Dhankhar and Kumar \cite{KD} to the broader setting of rational functions with fixed poles. Additionally, we establish corresponding results for such rational functions under suitable restrictions on their zeros. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16388 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inequalities For The Growth Of Rational Functions With Prescribed Poles Rather, N. A. Wani, Mohmmad Shafi Bhat, Danish Rashid Complex Variables 30A10, 30C10, 30C15 Let $\mathcal R_{n}$ be the set of all rational functions of the type $r(z) = f(z)/w(z)$, where $f(z)$ is a polynomial of degree at most $n$ and $w(z) = \prod_{j=1}^{n}(z-β_j)$, $|β_j|>1$ for $1\leq j\leq n$. In this work, we investigate the growth behavior of rational functions with prescribed poles by utilizing certain coefficients of the polynomial $f(z)$. The results obtained here not only refine and strengthen the findings of Rather et al. \cite{NS}, but also generalize recent growth estimates for polynomials due to Dhankhar and Kumar \cite{KD} to the broader setting of rational functions with fixed poles. Additionally, we establish corresponding results for such rational functions under suitable restrictions on their zeros. |
| title | Inequalities For The Growth Of Rational Functions With Prescribed Poles |
| topic | Complex Variables 30A10, 30C10, 30C15 |
| url | https://arxiv.org/abs/2602.16388 |