{"paper":{"title":"Explicit Teichm\\\"uller curves with complemetary series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Matheus, Gabriela Weitze-Schmith\\\"usen","submitted_at":"2011-09-02T18:33:14Z","abstract_excerpt":"We construct an explicit family of arithmetic Teichm\\\"uller curves $\\mathcal{C}_{2k}$, $k\\in\\mathbb{N}$, supporting $\\textrm{SL}(2,\\mathbb{R})$-invariant probabilities $\\mu_{2k}$ such that the associated $\\textrm{SL}(2,\\mathbb{R})$-representation on $L^2(\\mathcal{C}_{2k}, \\mu_{2k})$ has complementary series for every $k\\geq 3$. Actually, the size of the spectral gap along this family goes to zero. In particular, the Teichm\\\"uller geodesic flow restricted to these explicit arithmetic Teichm\\\"uller curves $\\mathcal{C}_{2k}$ has arbitrarily slow rate of exponential mixing."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0517","kind":"arxiv","version":3},"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"}