{"paper":{"title":"Fractal Weyl bounds and Hecke triangle groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Anke Pohl, Frederic Naud, Louis Soares","submitted_at":"2018-10-10T12:51:55Z","abstract_excerpt":"Let $\\Gamma_{w}$ be a non-cofinite Hecke triangle group with cusp width $w>2$ and let $\\varrho\\colon\\Gamma_w\\to U(V)$ be a finite-dimensional unitary representation of $\\Gamma_w$. In this note we announce a new fractal upper bound for the Selberg zeta function of $\\Gamma_{w}$ twisted by $\\varrho$. In strips parallel to the imaginary axis and bounded away from the real axis, the Selberg zeta function is bounded by $\\exp\\left( C_{\\varepsilon} \\vert s\\vert^{\\delta + \\varepsilon} \\right)$, where $\\delta = \\delta_{w}$ denotes the Hausdorff dimension of the limit set of $\\Gamma_{w}$. This bound impl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04489","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}