{"paper":{"title":"Joint distribution in residue classes of the base-$q$ and Ostrowski digital sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Divyum Sharma","submitted_at":"2017-10-26T19:04:11Z","abstract_excerpt":"Let $q$ be an integer $\\geq 2$ and let $S_q(n)$ denote the sum of digits of $n$ in base $q$. For\n  \\[\n  \\alpha=[0;\\overline{1,m}],\\ m\\geq 2,\n  \\] let $S_{\\alpha}(n)$ denote the sum of digits in the Ostrowski $\\alpha$-representation of $n$. Let $m_1,m_2\\geq 2$ be integers with $$\\gcd(q-1,m_1)=\\gcd(m,m_2)=1.$$ We prove that there exists $\\delta>0$ such that for all integers $a_1,a_2$,\n  \\begin{eqnarray*}\n  &&|\\{0\\leq n<N: S_{q}(n)\\equiv a_1\\pmod{m_1},\\ S_{\\alpha}(n)\\equiv a_2\\pmod{m_2}\\}|\n  &=&\\frac{N}{m_1m_2}+O(N^{1-\\delta}).\n  \\end{eqnarray*} The asymptotic relation implied by this equality wa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09873","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"}