{"paper":{"title":"The hybrid spectral test","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Peter Hellekalek","submitted_at":"2013-06-13T14:27:53Z","abstract_excerpt":"The starting point of this paper is the interplay between the construction principle of a sequence and the characters of the compact abelian group that underlies the construction. In case of the Halton sequence in base $\\mathbf b=(b_1, \\ldots, b_s)$ in the $s$-dimensional unit cube $[0,1)^s$, which is an important type of a digital sequence, this kind of duality principle leads to the so-called $\\mathbf b$-adic function system and provides the basis for the $\\mathbf b$-adic method, which we present in connection with hybrid sequences. This method employs structural properties of the compact gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3120","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"}