{"paper":{"title":"Discrepancy bounds for $\\boldsymbol{\\beta}$-adic Halton sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"J\\\"org M. Thuswaldner","submitted_at":"2016-10-17T13:42:15Z","abstract_excerpt":"Van der Corput and Halton sequences are well-known low-discrepancy sequences. Almost twenty years ago Ninomiya defined analogues of van der Corput sequences for $\\beta$-numeration and proved that they also form low-discrepancy sequences if $\\beta$ is a Pisot number. Only very recently Robert Tichy and his co-authors succeeded in proving that $\\boldsymbol{\\beta}$-adic Halton sequences are equidistributed for certain parameters $\\boldsymbol{\\beta}=(\\beta_1,\\ldots,\\beta_s)$ using methods from ergodic theory. In the present paper we continue this research and give discrepancy estimates for $\\bolds"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05107","kind":"arxiv","version":4},"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"}