{"paper":{"title":"Markov processes on the adeles and Dedekind's zeta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Roman Urban","submitted_at":"2011-06-28T10:27:22Z","abstract_excerpt":"Let $K$ be an algebraic number field. We construct an additive Markov process $X_t^{K_\\mathbb A}$ on the ring of adeles $K_\\mathbb A,$ whose coordinates $X_t^{(v)}$ are independent and use this process to give a probabilistic interpretation of the Dedekind zeta function $\\zeta_K(s),$ for $\\re s>1.$ This note extends a recent work of Yasuda [J. Theor. Probab. 23(3):748--769, 2010] where the case of the field $K=\\Q$ of rational numbers was considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5618","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"}