Partitions into powers of an algebraic number
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911879945781248 |
|---|---|
| author | Kala, Vítězslav Zindulka, Mikuláš |
| author_facet | Kala, Vítězslav Zindulka, Mikuláš |
| contents | We study partitions of complex numbers as sums of non-negative powers of a fixed algebraic number $β$. We prove that if $β$ is real quadratic, then the number of partitions is always finite if and only if some conjugate of $β$ is larger than 1. Further, we show that for $β$ satisfying a certain condition, the partition function attains all non-negative integers as values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_16688 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Partitions into powers of an algebraic number Kala, Vítězslav Zindulka, Mikuláš Number Theory 11P81, 11P84, 11R11 We study partitions of complex numbers as sums of non-negative powers of a fixed algebraic number $β$. We prove that if $β$ is real quadratic, then the number of partitions is always finite if and only if some conjugate of $β$ is larger than 1. Further, we show that for $β$ satisfying a certain condition, the partition function attains all non-negative integers as values. |
| title | Partitions into powers of an algebraic number |
| topic | Number Theory 11P81, 11P84, 11R11 |
| url | https://arxiv.org/abs/2305.16688 |