{"paper":{"title":"On the second moment and non-vanishing of central values of Hecke $L$-functions of $r$-th order characters","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Adrian Diaconu, Alexandru A. Popa, Bogdan Ion, Vicen\\c{t}iu Pa\\c{s}ol","submitted_at":"2026-07-29T17:01:57Z","abstract_excerpt":"In this paper, we establish asymptotic formulas for the first and second twisted moments of $r$-th order Hecke $L$-functions over global fields that contain the $2r$-th roots of unity, for $r\\ge 3$. We focus primarily on algebraic number fields. As a consequence, we establish a positive proportion of non-vanishing central values for these $L$-functions, specifically for families of both square-free and $r$-th power-free ideals. Our approach is based on the machinery of multiple Dirichlet series."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27131","kind":"arxiv","version":1},"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/2607.27131/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"}