Arithmetic properties of multiplier polynomials for certain polynomial maps
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913716983824384 |
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| author | Murakami, Yuya Sano, Kaoru Takehira, Kohei |
| author_facet | Murakami, Yuya Sano, Kaoru Takehira, Kohei |
| contents | We investigate the arithmetic properties of the multiplier polynomials for certain $1$-parameter families of polynomials. In particular, we prove integrality theorems of multiplier polynomials for $z^d+c$, $(z-c)z^d + c$ and $z^{d+1}+cz$. As a corollary, we obtain the uniform upper bound of the naive height of parabolic parameters of unicritical polynomials. Moreover, we determined the quadratic parabolic parameters for $z^2 + c$. We also conditionally list parabolic parameters for $z^2 + c$ of fixed degrees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17315 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arithmetic properties of multiplier polynomials for certain polynomial maps Murakami, Yuya Sano, Kaoru Takehira, Kohei Dynamical Systems Number Theory 32H50, 11R09 We investigate the arithmetic properties of the multiplier polynomials for certain $1$-parameter families of polynomials. In particular, we prove integrality theorems of multiplier polynomials for $z^d+c$, $(z-c)z^d + c$ and $z^{d+1}+cz$. As a corollary, we obtain the uniform upper bound of the naive height of parabolic parameters of unicritical polynomials. Moreover, we determined the quadratic parabolic parameters for $z^2 + c$. We also conditionally list parabolic parameters for $z^2 + c$ of fixed degrees. |
| title | Arithmetic properties of multiplier polynomials for certain polynomial maps |
| topic | Dynamical Systems Number Theory 32H50, 11R09 |
| url | https://arxiv.org/abs/2403.17315 |