{"paper":{"title":"Entire functions of exponential type represented by pseudo-random and random Taylor series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.PR","authors_text":"Alexander Borichev, Alon Nishry, Mikhail Sodin","submitted_at":"2014-09-09T13:51:01Z","abstract_excerpt":"We study the influence of the multipliers $\\xi (n)$ on the angular distribution of zeroes of the Taylor series \\[ F_\\xi (z) = \\sum_{n\\ge 0} \\xi (n) \\frac{z^n}{n!}\\,. \\] We show that the distribution of zeroes of $ F_\\xi $ is governed by certain autocorrelations of the sequence $ \\xi $. Using this guiding principle, we consider several examples of random and pseudo-random sequences $\\xi$ and, in particular, answer some questions posed by Chen and Littlewood in 1967.\n  As a by-product we show that if $\\xi$ is a stationary random integer-valued sequence, then either it is periodic, or its spectra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2736","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":""},"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"}