{"paper":{"title":"New zeta functions of Reidemeister type and twisted Burnside-Frobenius theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.RT"],"primary_cat":"math.GR","authors_text":"Alexander Fel'shtyn, Evgenij Troitsky, Malwina Zi\\k{e}tek","submitted_at":"2018-04-09T09:18:09Z","abstract_excerpt":"We introduce new zeta functions related to an endomorphism $\\phi$ of a discrete group $\\Gamma$. They are of two types: counting numbers of fixed ($\\rho\\sim \\rho\\circ\\phi^n$) irreducible representations for iterations of $\\phi$ from an appropriate dual space of $\\Gamma$ and counting Reidemeister numbers $R(\\phi^n)$ of different compactifications. Many properties of these functions and their coefficients are obtained. In many cases it is proved that these zeta functions coincide. The Gauss congruences are proved. Useful asymptotic formulas for the zeta functions are found. Rationality is proved "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02874","kind":"arxiv","version":2},"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"}