{"paper":{"title":"Uniform rationality of the Poincar\\'e series of definable, analytic equivalence relations on local fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Kien Huu Nguyen","submitted_at":"2016-10-25T16:28:36Z","abstract_excerpt":"Poincar\\'e series of $p$-adic, definable equivalence relations have been studied in various cases since Igusa's and Denef's work related to counting solutions of polynomial equations modulo $p^n$ for prime $p$. General semi-algebraic equivalence relations on local fields have been studied uniformly in $p$ recently in \\cite{16}. Here we generalize the rationality result of \\cite{16} to the analytic case, unifomly in $p$, building further on the appendix of \\cite{16} and on \\cite{13b}, \\cite{03}. In particular, the results hold for large positive characteristic local fields. We also introduce ra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07952","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"}