{"paper":{"title":"Divisor problem in arithmetic progressions modulo a prime power","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Igor E. Shparlinski, Kui Liu, Tianping Zhang","submitted_at":"2016-02-11T00:32:51Z","abstract_excerpt":"We obtain an asymptotic formula for the average value of the divisor function over the integers $n \\le x$ in an arithmetic progression $n \\equiv a \\pmod q$, where $q=p^k$ for a prime $p\\ge 3$ and a sufficiently large integer $k$. In particular, we break the classical barrier $q \\le x^{2/3}$ for such formulas, and generalise a recent result of R.~Khan (2015), making it uniform in $k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03583","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"}