Pfluger-type theorem for functions of refined regular growth
Journal Title: Математичні Студії - Year 2017, Vol 47, Issue 2
Abstract
Without a priori assumptions on zero distribution we prove that if an entire function f of noninteger order ρ has an asymptotic of the form log|f(reiθ)|=rρhf(θ)+O(rρδ(r)), E∌reiθ→∞, where h is the indicator of f, δ is an unbounded regularly growing function, and E is an appropriate exceptional set, then the counting function of zeros and the integrated counting function of zeros in the angle {z:α≤argz≤β} have similar asymptotic for almost all α≤β. It complements results on functions of completely regular growth due to P. Agranovich and V. Logvinenko, B. Vynnyts'kyi and R. Khats'.
Authors and Affiliations
Igor Chyzhykov
Keywords
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- EP ID EP310104
- DOI 10.15330/ms.47.2.169-178
- Views 40
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