{"paper":{"title":"The Geometry of p-Adic Fractal Strings: A Comparative Survey","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.GT","math.NT"],"primary_cat":"math.MG","authors_text":"Hung Lu, Michel L. Lapidus","submitted_at":"2011-05-15T20:26:04Z","abstract_excerpt":"We give a brief overview of the theory of complex dimensions of real (archimedean) fractal strings via an illustrative example, the ordinary Cantor string, and a detailed survey of the theory of p-adic (nonarchimedean) fractal strings and their complex dimensions. Moreover, we present an explicit volume formula for the tubular neighborhood of a p-adic fractal string Lp, expressed in terms of the underlying complex dimensions. Special attention will be focused on p-adic self-similar strings, in which the nonarchimedean theory takes a more natural form than its archimedean counterpart. In contra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2966","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"}