Isomorphisms between eigenspaces of slow and fast transfer operators Article Swipe
For any Hecke triangle surface $\Gamma\backslash\mathbb{H}$ of finite or infinite area and any finite-dimensional unitary representation $\chi$ of the Hecke triangle group $\Gamma$ there had been constructed two families of Ruelle-like transfer operators parametrized by $\mathbb{C}$. The eigenfunctions with eigenvalue $1$ of the transfer operators ${\mathcal L}_s^\text{fast}$ of the one family determine the zeros of the Selberg zeta function for $(\Gamma,\chi)$. Further, if $\Gamma\backslash\mathbb{H}$ is cofinite and $\chi$ is trivial, the eigenfunctions with eigenvalue $1$ of a certain regularity of the transfer operators ${\mathcal L}_s^\text{slow}$ in the other family characterize the Maass cusp forms for $\Gamma$. In this article we characterize this eigenspace of ${\mathcal L}_s^\text{fast}$ as an eigenspace with eigenvalue $1$ of ${\mathcal L}_s^\text{slow}$, and vice versa. This solves a conjecture by the second author and M. M\oller.
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- Type
- preprint
- Language
- en
- Landing Page
- https://arxiv.org/abs/1606.09109v1
- OA Status
- green
- References
- 6
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2460426957
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https://openalex.org/W2460426957Canonical identifier for this work in OpenAlex
- Title
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Isomorphisms between eigenspaces of slow and fast transfer operatorsWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2016Year of publication
- Publication date
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2016-06-29Full publication date if available
- Authors
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Alexander Adam, Anke PohlList of authors in order
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https://arxiv.org/abs/1606.09109v1Publisher landing page
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/abs/1606.09109v1Direct OA link when available
- Concepts
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Eigenfunction, Cusp (singularity), Eigenvalues and eigenvectors, Mathematics, Conjecture, Transfer (computing), Combinatorics, Transfer operator, Backslash, Unitary representation, Cusp form, Pure mathematics, Physics, Geometry, Quantum mechanics, Lie group, Computer science, Parallel computingTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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20Other works algorithmically related by OpenAlex
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