{"paper":{"title":"An extended Vinogradov's mean value theorem","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Changkeun Oh, Kiseok Yeon","submitted_at":"2025-06-02T14:59:11Z","abstract_excerpt":"In this paper, we provide novel mean value estimates for exponential sums related to the extended main conjecture of Vinogradov's mean value theorem, by developing the Hardy-Littlewood circle method together with a refined shifting variables argument. Let $d\\geq 2$ be a natural number and $\\boldsymbol{\\alpha}=(\\alpha_d,\\ldots, \\alpha_1)\\in \\mathbb{R}^d.$ Define the exponential sum \\begin{equation*}\n  f_d(\\boldsymbol{\\alpha};N):=\\sum_{1 \\leq n \\leq N}e(\\alpha_d n^d + \\cdots+ \\alpha_1 n). \\end{equation*} For $p>0$, consider mean values of the exponential sums \\begin{equation*}\n  \\mathcal{I}_{p,d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01751","kind":"arxiv","version":2},"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/2506.01751/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"}