Semantic Scholar Open Access 2025

Sharp bounds for the valence of certain logharmonic polynomials

Kirill Lazebnik Erik Lundberg

Abstrak

Consider a logharmonic polynomial; that is, a product of the form $p(z)\overline{q(z)}$, where $p$, $q$ are holomorphic polynomials. Assume $q$ is linear and denote by $n$ the degree of $p$. It was recently shown in arXiv:2302.04339 [math.CV] that the valence of such a logharmonic polynomial is at most $3n-1$; in this paper we show that their $3n-1$ upper bound is sharp. Together with the work of arXiv:2302.04339 [math.CV], this resolves a conjecture of Bshouty and Hengartner.

Topik & Kata Kunci

Mathematics

Penulis (2)

Kirill Lazebnik

Erik Lundberg

Format Sitasi

APA MLA BibTeX

Lazebnik, K., Lundberg, E. (2025). Sharp bounds for the valence of certain logharmonic polynomials. https://doi.org/10.1090/proc/17674

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Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: Semantic Scholar
DOI: 10.1090/proc/17674
Akses: Open Access ✓