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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.01586 |
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| _version_ | 1866911367040073728 |
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| author | Dang, Nguyen Viet Lin, Jiasheng Naud, Frédéric |
| author_facet | Dang, Nguyen Viet Lin, Jiasheng Naud, Frédéric |
| contents | Let $(M,g)$ be some smooth, closed, compact Riemannian manifold and $(M_N\mapsto M)_N$ be an increasing sequence of large degree cyclic covers of $M$ that converges when $N\rightarrow +\infty$, in a suitable sense, to some limit $\mathbb{Z}^p$ cover $M_\infty$ over $M$. Motivated by recent works on zeta determinants on random surfaces and some natural questions in Euclidean quantum field theory, we show the convergence of the sequence $ \frac{\log\det_ζ(Δ_{N})}{\text{Vol}(M_N)} $ when $N\rightarrow +\infty$ where $Δ_N$ is the Laplace-Beltrami operator on $M_N$. We also generalize our results to the case of twisted Laplacians coming from certain flat unitary vector bundles over $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01586 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotics of zeta determinants of Laplacians on large degree abelian covers Dang, Nguyen Viet Lin, Jiasheng Naud, Frédéric Mathematical Physics 58C40 58J50 58J52 11M36 81T20 Let $(M,g)$ be some smooth, closed, compact Riemannian manifold and $(M_N\mapsto M)_N$ be an increasing sequence of large degree cyclic covers of $M$ that converges when $N\rightarrow +\infty$, in a suitable sense, to some limit $\mathbb{Z}^p$ cover $M_\infty$ over $M$. Motivated by recent works on zeta determinants on random surfaces and some natural questions in Euclidean quantum field theory, we show the convergence of the sequence $ \frac{\log\det_ζ(Δ_{N})}{\text{Vol}(M_N)} $ when $N\rightarrow +\infty$ where $Δ_N$ is the Laplace-Beltrami operator on $M_N$. We also generalize our results to the case of twisted Laplacians coming from certain flat unitary vector bundles over $M$. |
| title | Asymptotics of zeta determinants of Laplacians on large degree abelian covers |
| topic | Mathematical Physics 58C40 58J50 58J52 11M36 81T20 |
| url | https://arxiv.org/abs/2505.01586 |