{"paper":{"title":"Sums of almost equal squares of primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Angel Kumchev, Taiyu Li","submitted_at":"2011-09-26T15:06:37Z","abstract_excerpt":"We study the representations of large integers $n$ as sums $p_1^2 + ... + p_s^2$, where $p_1,..., p_s$ are primes with $| p_i - (n/s)^{1/2} | \\le n^{\\theta/2}$, for some fixed $\\theta < 1$. When $s = 5$ we use a sieve method to show that all sufficiently large integers $n \\equiv 5 \\pmod {24}$ can be represented in the above form for $\\theta > 8/9$. This improves on earlier work by Liu, L\\\"{u} and Zhan, who established a similar result for $\\theta > 9/10$. We also obtain estimates for the number of integers $n$ satisfying the necessary local conditions but lacking representations of the above f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5594","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"}