{"paper":{"title":"Power sums and Siegel-type zero-free regions for L-functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jesse Thorner","submitted_at":"2026-08-12T17:00:49Z","abstract_excerpt":"Let $\\pi$ and $\\pi'$ be unitary cuspidal automorphic representations of $\\mathrm{GL}(n)$ and $\\mathrm{GL}(n')$ over a number field $F$. Let $\\mathfrak{C}_{\\pi}$ be the analytic conductor of $\\pi$. We develop a new approach to zero-free regions for $L$-functions via lower bounds for power sums, proving for all $\\varepsilon>0$ the existence of ineffective constants $c=c_{n,F,\\varepsilon}>0$ and $c'=c'_{n,F,\\pi',\\varepsilon}>0$ such that the standard $L$-function $L(s,\\pi)$ satisfies \\[ |L(\\sigma+it,\\pi)|\\geq c(\\mathfrak{C}_{\\pi}(|t|+3))^{-\\varepsilon},\\qquad \\sigma\\geq 1-c(\\mathfrak{C}_{\\pi}(|t|"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12257","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/2608.12257/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"}