{"paper":{"title":"Simple zeros of primitive Dirichlet $L$-functions and the asymptotic large sieve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Maksym Radziwi\\l\\l, Sheng-chi Liu, Vorrapan Chandee, Yoonbok Lee","submitted_at":"2012-11-28T20:08:15Z","abstract_excerpt":"Assuming the Generalized Riemann Hypothesis (GRH), we show using the asymptotic large sieve that 91% of the zeros of primitive Dirichlet $L$-functions are simple. This improves on earlier work of \\\"{O}zl\\\"{u}k which gives a proportion of at most 86%. We further compute an $q$-analogue of the Pair Correlation Function $F(\\alpha)$ averaged over all primitive Dirichlet $L$-functions in the range $|\\alpha| < 2$ . Previously such a result was available only when the average included all the characters $\\chi$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6725","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"}