{"paper":{"title":"Limiting distribution of eigenvalues in the large sieve matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Florin P. Boca, Maksym Radziwi{\\l}{\\l}","submitted_at":"2016-09-19T18:11:56Z","abstract_excerpt":"The large sieve inequality is equivalent to the bound $\\lambda_1 \\leqslant N + Q^2-1$ for the largest eigenvalue $\\lambda_1$ of the $N$ by $N$ matrix $A^{\\star} A$, naturally associated to the positive definite quadratic form arising in the inequality. For arithmetic applications the most interesting range is $N \\asymp Q^2$. Based on his numerical data Ramar\\'e conjectured that when $N \\sim \\alpha Q^2$ as $Q \\rightarrow \\infty$ for some finite positive constant $\\alpha$, the limiting distribution of the eigenvalues of $A^{\\star} A$, scaled by $1/N$, exists and is non-degenerate.\n  In this pape"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05843","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"}