Dirichlet dynamical zeta function for billiard flow
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908371674726400 |
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| author | Petkov, Vesselin |
| author_facet | Petkov, Vesselin |
| contents | We study the Dirichlet dynamical zeta function $η_D(s)$ for billiard flow corresponding to several strictly convex disjoint obstacles. For large ${\rm Re}\: s$ we have $η_D(s) =\sum_{n= 1}^{\infty} a_n e^{-λ_n s}, \: a_n \in \mathbb R$ and $η_D$ admits a meromorphic continuation to $\mathbb C$. We obtain some conditions of the frequencies $λ_n$ and some sums of coefficients $a_n$ which imply that $η_D$ cannot be prolonged as entire function. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_03818 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dirichlet dynamical zeta function for billiard flow Petkov, Vesselin Dynamical Systems Number Theory 37D20, 37D40, 11M41, 11M36 We study the Dirichlet dynamical zeta function $η_D(s)$ for billiard flow corresponding to several strictly convex disjoint obstacles. For large ${\rm Re}\: s$ we have $η_D(s) =\sum_{n= 1}^{\infty} a_n e^{-λ_n s}, \: a_n \in \mathbb R$ and $η_D$ admits a meromorphic continuation to $\mathbb C$. We obtain some conditions of the frequencies $λ_n$ and some sums of coefficients $a_n$ which imply that $η_D$ cannot be prolonged as entire function. |
| title | Dirichlet dynamical zeta function for billiard flow |
| topic | Dynamical Systems Number Theory 37D20, 37D40, 11M41, 11M36 |
| url | https://arxiv.org/abs/2501.03818 |