{"paper":{"title":"Zeros of Polynomials in Derivatives of Automorphic $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandru Zaharescu, Anji Dong, Nawapan Wattanawanichkul","submitted_at":"2025-12-27T03:40:38Z","abstract_excerpt":"Let $\\mathfrak{F}_m$ be the set of all cuspidal automorphic representations of $\\mathrm{GL}_m(\\mathbb{A}_{\\mathbb{Q}})$, and let $F(s,\\boldsymbol{\\pi})$ be a polynomial in the derivatives of $L$-functions associated with representations $\\pi \\in \\cup_{m=1}^{\\infty} \\mathfrak{F}_m$. We establish an asymptotic formula for the number of nontrivial zeros of $F(s,\\boldsymbol{\\pi})$ with $0 < \\operatorname{Im}(s) < T$. We explicitly determine the main term of this formula in terms of the dimensions, the arithmetic conductors, and the orders of differentiation of the component $L$-functions. Furtherm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.22451","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.22451/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"}