On the generating series of the degree sequence
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909829997527040 |
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| author | Nguyen, Quang-Khai |
| author_facet | Nguyen, Quang-Khai |
| contents | We study the generating series associated with the degree sequence of a monomial self-map of a projective toric variety. We establish conditions under which this series has its circle of convergence as a natural boundary, and hence is a transcendental, non-holonomic function. In the case of toric surfaces, our results are sharp; moreover, we answer a question of Bell by proving that their reductions modulo $p$ are transcendental for all but finitely many prime numbers $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06142 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the generating series of the degree sequence Nguyen, Quang-Khai Dynamical Systems Algebraic Geometry Number Theory We study the generating series associated with the degree sequence of a monomial self-map of a projective toric variety. We establish conditions under which this series has its circle of convergence as a natural boundary, and hence is a transcendental, non-holonomic function. In the case of toric surfaces, our results are sharp; moreover, we answer a question of Bell by proving that their reductions modulo $p$ are transcendental for all but finitely many prime numbers $p$. |
| title | On the generating series of the degree sequence |
| topic | Dynamical Systems Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2510.06142 |