On the number of roots for harmonic trinomials
| Autor: | Barrera, Gerardo, Barrera, Waldemar, Navarrete, Juan Pablo |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Journal of Mathematical Analysis and Applications 2022, Volume 514, Number 2, 126313 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jmaa.2022.126313 |
| Popis: | In this manuscript we study the counting problem for harmonic trinomials of the form $a\zeta^n+b\overline{\zeta}^m+c$, where $n,m\in \mathbb{N}$, $n>m$, and $a$, $b$ and $c$ are non-zero complex numbers. As a consequence, we obtain the Fundamental Theorem of Algebra and the Wilmshurst conjecture for harmonic trinomials. The proof of the counting problem relies on the Bohl method introduced in Bohl (1908). Comment: 14 pages |
| Databáze: | arXiv |
| Externí odkaz: |
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