{"paper":{"title":"Arithmetic properties and zeros of the Bergman kernel on a class of quotient domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Luke D. Edholm, Vikram T. Mathew","submitted_at":"2025-05-26T19:49:17Z","abstract_excerpt":"An effective formula for the Bergman kernel on $\\mathbb{H}_{\\gamma} = \\{|z_1|^\\gamma < |z_2| < 1 \\}$ is obtained for rational $\\gamma = \\frac{m}{n} >1$. The formula depends on arithmetic properties of $\\gamma$, which uncovers new symmetries and clarifies previous results. The formulas are then used to study the Lu Qi-Keng problem. We produce sequences of rationals $\\gamma_j \\searrow 1$, where each $\\mathbb{H}_{\\gamma_j}$ has a Bergman kernel with zeros (while $\\mathbb{H}_1$ is known to have a zero-free kernel), resolving an open question on this domain class."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.20489","kind":"arxiv","version":3},"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/2505.20489/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"}