{"paper":{"title":"Low lying zeros of L-functions with orthogonal symmetry","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.NT","authors_text":"C. P. Hughes, Steven J. Miller","submitted_at":"2005-07-21T19:38:02Z","abstract_excerpt":"We investigate the moments of a smooth counting function of the zeros near the central point of L-functions of weight k cuspidal newforms of prime level N. We split by the sign of the functional equations and show that for test functions whose Fourier transform is supported in (-1/n, 1/n), as N --> oo the first n centered moments are Gaussian. By extending the support to (-1/n-1, 1/n-1), we see non-Gaussian behavior; in particular the odd centered moments are non-zero for such test functions. If we do not split by sign, we obtain Gaussian behavior for support in (-2/n, 2/n) if 2k >= n. The nth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0507450","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"}