Lower bounds for resonances of infinite-area Riemann surfaces
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Bibliographic record
Abstract
Abstract. For infinite area, geometrically finite surfaces X = Γ\\H 2, we prove new lower bounds on the local density of resonances D(z) when z lies in a logarithmic neighborhood of the real axis. These lower bounds involve the dimension δ of the limit set of Γ. The first bound is valid when δ> 1 2 and shows logarithmic growth of the number D(z) of resonances at high energy i.e. when |Re(z) | → +∞. The second bound holds for δ> 3 and if Γ is an infinite index subgroup of certain 4 arithmetic groups. In this case we obtain a polynomial lower bound. Both results are in favor of a conjecture of Guillopé-Zworski on the existence of a fractal Weyl law for resonances. 1. Introduction and
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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