{"paper":{"title":"Multiple recurrence and convergence along the primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Tamar D. Ziegler, Trevor D. Wooley","submitted_at":"2010-01-22T21:18:47Z","abstract_excerpt":"Let $E\\subset \\mathbb Z$ be a set of positive upper density. Suppose that $P_1,P_2,..., P_k\\in \\mathbb Z[X]$ are polynomials having zero constant terms. We show that the set $E\\cap (E-P_1(p-1))\\cap ... \\cap (E-P_k(p-1))$ is non-empty for some prime number $p$. Furthermore, we prove convergence in $L^2$ of polynomial multiple averages along the primes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.4081","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":""},"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"}