Work

Arithmetic properties of multiplier polynomials for certain polynomial maps

Year: 2026

Type: article

Abstract: In this paper, we investigate the arithmetic properties of the multiplier polynomials for certain [Formula: see text]-parameter families of polynomials. In particular, we prove integrality theorems about the multiplier polynomials for [Formula: see text], [Formula: see text] and [Formula: see text]. As a corollary, we obtain a uniform upper bound on the naive height of parabolic parameters for unicritical polynomials. Moreover, we determine the quadratic parabolic parameters for [Formula: see text]. We also conditionally list the parabolic parameters for [Formula: see text] of certain fixed degrees.

Source: International Journal of Number Theory

DOI: 10.1142/s1793042126501381

Authors: Yuya Murakami, Kaoru Sano, Kohei Takehira

Institutions: Kyushu University, NTT (Japan), Tohoku University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Tohoku University

OpenAlex ID: W4393284303

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