Dynamical systems defined by polynomials with algebraic properties
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916029489217536 |
|---|---|
| author | Akiyama, Shigeki Gao, Xiang Kamae, Teturo |
| author_facet | Akiyama, Shigeki Gao, Xiang Kamae, Teturo |
| contents | Let (x_n; n\in Z) be a bisequence of elements x_n in the 1-dimensional torus R/Z, which is called a stream over R/Z. Let P(z)=a_k z^k+...+a_1 z+a_0 be a polynomial with integer coefficients. Define the set of streams over R/Z such that the convolution product P(z)\times(x_n; n\in Z)=(\sum_{i=0}^k a_i x_{n-i}; n\in Z)=(0; n\in Z), which is called the stream 0 of P. We study similarities between stream 0 of P and the roots of P(z)=0. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12888 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamical systems defined by polynomials with algebraic properties Akiyama, Shigeki Gao, Xiang Kamae, Teturo Number Theory Let (x_n; n\in Z) be a bisequence of elements x_n in the 1-dimensional torus R/Z, which is called a stream over R/Z. Let P(z)=a_k z^k+...+a_1 z+a_0 be a polynomial with integer coefficients. Define the set of streams over R/Z such that the convolution product P(z)\times(x_n; n\in Z)=(\sum_{i=0}^k a_i x_{n-i}; n\in Z)=(0; n\in Z), which is called the stream 0 of P. We study similarities between stream 0 of P and the roots of P(z)=0. |
| title | Dynamical systems defined by polynomials with algebraic properties |
| topic | Number Theory |
| url | https://arxiv.org/abs/2502.12888 |