{"paper":{"title":"On Vinogradov's mean value theorem: strongly diagonal behaviour via efficient congruencing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kevin Ford, Trevor D. Wooley","submitted_at":"2013-04-25T14:14:55Z","abstract_excerpt":"We enhance the efficient congruencing method for estimating Vinogradov's integral for moments of order $2s$, with $1\\le s\\le k^2-1$. In this way, we prove the main conjecture for such even moments when $1\\le s\\le \\tfrac{1}{4}(k+1)^2$, showing that the moments exhibit strongly diagonal behaviour in this range. There are improvements also for larger values of $s$, these finding application to the asymptotic formula in Waring's problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6917","kind":"arxiv","version":3},"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"}