{"paper":{"title":"p-adic entropy and a p-adic Fuglede-Kadison determinant","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"C. Deninger","submitted_at":"2006-08-22T11:12:32Z","abstract_excerpt":"Using periodic points we study a notion of entropy with values in the p-adic numbers. This is done for actions of countable discrete residually finite groups $\\Gamma$. For suitable $\\Gamma = \\mathbb{Z}^d$-actions we obtain p-adic analogues of multivariable Mahler measures. For certain actions of more general groups the p-adic entropy can be expressed in terms of a p-adic analogue of the Fuglede-Kadison determinant from the theory of von Neumann algebras. Many basic questions remain open."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608539","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"}