{"paper":{"title":"A hybrid inequality of Erd\\\"os-Tur\\'an-Koksma for digital sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Peter Hellekalek","submitted_at":"2012-11-08T09:39:01Z","abstract_excerpt":"For bases $\\mathbf{b}=(b_1,..., b_s)$ of $s$ not necessarily distinct integers $b_i\\ge 2$, we prove a version of the inequality of \\etk \\ for the hybrid function system composed of the Walsh functions in base $\\bfb^{(1)}=(b_1,..., b_{s_1})$ and, as second component, the $\\bfb^{(2)}$-adic functions, $\\bfb^{(2)}=(b_{s_1+1},..., b_s)$, with $s=s_1+s_2$, $s_1$ and $s_2$ not both equal to 0. Further, we point out why this choice of a hybrid function system covers all possible cases of sequences that employ addition of digit vectors as their main construction principle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1804","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"}