{"paper":{"title":"Exponential polynomials in the oscillation theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ilpo Laine, Janne Heittokangas, Katsuya Ishizaki, Kazuya Tohge","submitted_at":"2019-07-18T10:55:28Z","abstract_excerpt":"Supposing that $A(z)$ is an exponential polynomial of the form\n  $$\n  A(z)=H_0(z)+H_1(z)e^{\\zeta_1z^n}+\\cdots +H_m(z)e^{\\zeta_mz^n},\n  $$ where $H_j$'s are entire and of order $<n$, it is demonstrated that the function $H_0(z)$ and the geometric location of the leading coefficients $\\zeta_1,\\ldots,\\zeta_m$ play a key role in the oscillation of solutions of the differential equation $f''+A(z)f=0$. The key tools consist of value distribution properties of exponential polynomials, and elementary properties of the Phragm\\'en-Lindel\\\"of indicator function. In addition to results in the whole comple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07984","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":""},"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"}