{"paper":{"title":"The asymptotic number of zeros of exponential sums in critical strips","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CV","authors_text":"J. Heittokangas, Z.-T. Wen","submitted_at":"2019-08-26T06:25:39Z","abstract_excerpt":"Normalized exponential sums are entire functions of the form\n  $$\n  f(z)=1+H_1e^{w_1z}+\\cdots+H_ne^{w_nz},\n  $$ where $H_1,\\ldots, H_n\\in\\C$ and $0<w_1<\\ldots<w_n$. It is known that the zeros of such functions are in finitely many vertical strips $S$. The asymptotic number of the zeros in the union of all these strips was found by R. E. Langer already in 1931. In 1973, C. J. Moreno proved that there are zeros arbitrarily close to any vertical line in any strip $S$, provided that $1,w_1,\\ldots,w_n$ are linearly independent over the rational numbers. In this study the asymptotic number of zeros "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09491","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/1908.09491/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"}