{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:7YH7O2CFL6YG5F52PRQDXIWYUZ","short_pith_number":"pith:7YH7O2CF","schema_version":"1.0","canonical_sha256":"fe0ff768455fb06e97ba7c603ba2d8a657027e55895e1fea06a2f8481094fd1d","source":{"kind":"arxiv","id":"1710.09873","version":1},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1710.09873","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-26T19:04:11Z","cross_cats_sorted":[],"title_canon_sha256":"c3208f2cbb665ef5ce20c6408cd9bedbe455b7a83a427851e268b42d4fe89c07","abstract_canon_sha256":"1e41b1a6d19370c7b64e7a1049430982ab2972924fe236fd0606086b1e4135cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:55.302446Z","signature_b64":"9U84stUK1y3Zvh/RtgLgCiinS4m6XhfAuLipfWEzvLbW4O3FEqNtONvvxMv1a//HitozTjI/troBaRSTF8ulDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe0ff768455fb06e97ba7c603ba2d8a657027e55895e1fea06a2f8481094fd1d","last_reissued_at":"2026-05-18T00:31:55.302042Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:55.302042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1710.09873","created_at":"2026-05-18T00:31:55.302097+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.09873v1","created_at":"2026-05-18T00:31:55.302097+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09873","created_at":"2026-05-18T00:31:55.302097+00:00"},{"alias_kind":"pith_short_12","alias_value":"7YH7O2CFL6YG","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"7YH7O2CFL6YG5F52","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"7YH7O2CF","created_at":"2026-05-18T12:31:05.417338+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7YH7O2CFL6YG5F52PRQDXIWYUZ","json":"https://pith.science/pith/7YH7O2CFL6YG5F52PRQDXIWYUZ.json","graph_json":"https://pith.science/api/pith-number/7YH7O2CFL6YG5F52PRQDXIWYUZ/graph.json","events_json":"https://pith.science/api/pith-number/7YH7O2CFL6YG5F52PRQDXIWYUZ/events.json","paper":"https://pith.science/paper/7YH7O2CF"},"agent_actions":{"view_html":"https://pith.science/pith/7YH7O2CFL6YG5F52PRQDXIWYUZ","download_json":"https://pith.science/pith/7YH7O2CFL6YG5F52PRQDXIWYUZ.json","view_paper":"https://pith.science/paper/7YH7O2CF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.09873&json=true","fetch_graph":"https://pith.science/api/pith-number/7YH7O2CFL6YG5F52PRQDXIWYUZ/graph.json","fetch_events":"https://pith.science/api/pith-number/7YH7O2CFL6YG5F52PRQDXIWYUZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7YH7O2CFL6YG5F52PRQDXIWYUZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7YH7O2CFL6YG5F52PRQDXIWYUZ/action/storage_attestation","attest_author":"https://pith.science/pith/7YH7O2CFL6YG5F52PRQDXIWYUZ/action/author_attestation","sign_citation":"https://pith.science/pith/7YH7O2CFL6YG5F52PRQDXIWYUZ/action/citation_signature","submit_replication":"https://pith.science/pith/7YH7O2CFL6YG5F52PRQDXIWYUZ/action/replication_record"}},"created_at":"2026-05-18T00:31:55.302097+00:00","updated_at":"2026-05-18T00:31:55.302097+00:00"}