{"paper":{"title":"Compact Open Spectral Sets In $\\mathbb{Q}_p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Aihua Fan, Ruxi Shi, Shilei Fan","submitted_at":"2015-11-16T06:20:09Z","abstract_excerpt":"In this article, we prove that a compact open set in the field $\\mathbb{Q}_p$ of $p$-adic numbers is a spectral set if and only if it tiles $\\mathbb{Q}_p$ by translation, and also if and only if it is $p$-homogeneous which is easy to check. We also characterize spectral sets in $\\mathbb{Z}/p^n \\mathbb{Z}$ ($p\\ge 2$ prime, $n\\ge 1$ integer) by tiling property and also by homogeneity. Moreover, we construct a class of singular spectral measures in $\\mathbb{Q}_p$, some of which are self-similar measures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04837","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"}