{"paper":{"title":"Moments of Higher derivatives of the logarithmic derivative of Dirichlet $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Samprit Ghosh","submitted_at":"2025-09-08T07:21:02Z","abstract_excerpt":"Let $\\chi$ be a non-principal Dirichlet character and $L(s, \\chi)$ be the associated Dirichlet $L$-function. Let us use $\\mathcal{L}(s,\\chi)$ to denote its logarithmic derivative $L'(s, \\chi)/L(s, \\chi)$. We first prove some arithmetic formulas for higher derivatives $\\mathcal{L}^{(r)}(1,\\chi)$. We then investigate their moments. We study the average of $P^{(a,b)}(\\mathcal{L}^{(r)}(1,\\chi))$ as $\\chi$ runs over all non-principal Dirichlet characters with a given large prime conductor $m$, where $P^{(a,b)}(z) = z^a \\overline{z}^b$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.06390","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/2509.06390/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"}