{"paper":{"title":"On the divisor problem with congruence conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lirui Jia, Tianxin Cai, Wenguang Zhai","submitted_at":"2019-08-14T07:18:08Z","abstract_excerpt":"Let $d(n; r_1, q_1, r_2, q_2)$ be the number of factorization $n=n_1n_2$ satisfying $n_i\\equiv r_i\\pmod{q_i}$ ($i=1,2$) and $\\Delta(x; r_1, q_1, r_2, q_2)$ be the error term of the summatory function of $d(n; r_1, q_1, r_2, q_2)$ with $x\\geq (q_1q_2)^{1+\\varepsilon}, 1\\leq r_i\\leq q_i$, and $(r_i, q_i)=1$ ($i=1, 2$). We study the power moments and sign changes of $\\Delta(x; r_1, q_1, r_2, q_2)$, and prove that for a sufficiently large constant $C$, $\\Delta(q_1q_2x; r_1, q_1, r_2, q_2)$ changes sign in the interval $[T,T+C\\sqrt{T}]$ for any large $T$. Meanwhile, we show that for a small constan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05598","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.05598/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}