{"paper":{"title":"Symmetries of the transfer operator for $\\Gamma_0(N)$ and a character deformation of the Selberg zeta function for $\\Gamma_0(4)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP","math.SP"],"primary_cat":"math.NT","authors_text":"Dieter Mayer, Markus Fraczek","submitted_at":"2010-11-19T14:57:14Z","abstract_excerpt":"The transfer operator for $\\Gamma_0(N)$ and trivial character $\\chi_0$ possesses a finite group of symmetries generated by permutation matrices $P$ with $P^2=id$. Every such symmetry leads to a factorization of the Selberg zeta function in terms of Fredholm determinants of a reduced transfer operator. These symmetries are related to the group of automorphisms in $GL(2,\\mathbb{Z})$ of the Maass wave forms of $\\Gamma_0(N)$ . For the group $\\Gamma_0(4)$ and Selberg's character $\\chi_\\alpha$ there exists just one non-trivial symmetry operator $P$. The eigenfunctions of the corresponding reduced tr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4441","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"}