{"paper":{"title":"On sums of powers of almost equal primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Angel Kumchev, Huafeng Liu","submitted_at":"2016-08-27T19:29:58Z","abstract_excerpt":"Let $k \\ge 2$ and $s$ be positive integers, and let $n$ be a large positive integer subject to certain local conditions. We prove that if $s \\ge k^2+k+1$ and $\\theta > 31/40$, then $n$ can be expressed as a sum $p_1^k + \\dots + p_s^k$, where $p_1, \\dots, p_s$ are primes with $|p_j - (n/s)^{1/k}| \\le n^{\\theta/k}$. This improves on earlier work by Wei and Wooley and by Huang who proved similar theorems when $\\theta > 19/24$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07735","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"}