{"paper":{"title":"Generalization of P\\'olya's zero distribution theory for exponential polynomials, plus sharp results for asymptotic growth","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Janne Heittokangas, Zhi-Tao Wen","submitted_at":"2019-05-22T01:58:32Z","abstract_excerpt":"An exponential polynomial of order $q$ is an entire function of the form\n  $$\n  f(z)=P_1(z)e^{Q_1(z)}+\\cdots +P_k(z)e^{Q_k(z)},\n  $$ where the coefficients $P_j(z),Q_j(z)$ are polynomials in $z$ such that\n  $$\n  \\max\\{\\deg{Q_j}\\}=q.\n  $$ In 1977 Steinmetz proved that the zeros of $f$ lying outside of finitely many logarithmic strips around so called critical rays have exponent of convergence $\\leq q-1$. This result does not say nothing about the zero distribution of $f$ in each individual logarithmic strip. Here, it is shown that the asymptotic growth of the non-integrated counting function of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08919","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":""},"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"}