Fractal Weyl bounds and Hecke triangle groups Article Swipe
Frédéric Naud
,
Anke Pohl
,
Louis Soares
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.3934/era.2019.26.003
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.3934/era.2019.26.003
Let $Γ_{w}$ be a non-cofinite Hecke triangle group with cusp width $w>2$ and let $\varrho\colonΓ_w\to U(V)$ be a finite-dimensional unitary representation of $Γ_w$. In this note we announce a new fractal upper bound for the Selberg zeta function of $Γ_{w}$ twisted by $\varrho$. In strips parallel to the imaginary axis and bounded away from the real axis, the Selberg zeta function is bounded by $\exp\left( C_{\varepsilon} \vert s\vert^{δ+ \varepsilon} \right)$, where $δ= δ_{w}$ denotes the Hausdorff dimension of the limit set of $Γ_{w}$. This bound implies fractal Weyl bounds on the resonances of the Laplacian for all geometrically finite surfaces $X=\widetildeΓ\backslash\mathbb{H}$ where $\widetildeΓ$ is a finite index, torsion-free subgroup of $Γ_w$.
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- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.3934/era.2019.26.003
- OA Status
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- Cited By
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- 19
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- OpenAlex ID
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Fractal Weyl bounds and Hecke triangle groupsWork title
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preprintOpenAlex work type
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enPrimary language
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2019Year of publication
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2019-01-01Full publication date if available
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Frédéric Naud, Anke Pohl, Louis SoaresList of authors in order
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https://doi.org/10.3934/era.2019.26.003Publisher landing page
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YesWhether a free full text is available
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diamondOpen access status per OpenAlex
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Mathematics, Combinatorics, Bounded function, Hausdorff dimension, Exponent, Cusp (singularity), Upper and lower bounds, Cusp form, Mathematical analysis, Geometry, Philosophy, LinguisticsTop concepts (fields/topics) attached by OpenAlex
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1Total citation count in OpenAlex
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| abstract_inverted_index.$\varrho$. | 42 |
| abstract_inverted_index.resonances | 91 |
| abstract_inverted_index.$\exp\left( | 64 |
| abstract_inverted_index.s\vert^{δ+ | 67 |
| abstract_inverted_index.\varepsilon} | 68 |
| abstract_inverted_index.non-cofinite | 4 |
| abstract_inverted_index.torsion-free | 107 |
| abstract_inverted_index.geometrically | 97 |
| abstract_inverted_index.$\widetildeΓ$ | 102 |
| abstract_inverted_index.representation | 20 |
| abstract_inverted_index.C_{\varepsilon} | 65 |
| abstract_inverted_index.finite-dimensional | 18 |
| abstract_inverted_index.$\varrho\colonΓ_w\to | 14 |
| abstract_inverted_index.$X=\widetildeΓ\backslash\mathbb{H}$ | 100 |
| cited_by_percentile_year.max | 93 |
| cited_by_percentile_year.min | 89 |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.55370459 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |