On the connection between the growth of zeros and the decrease of Taylor coefficients of entire functions

DOI10.1134/S0001434623010042MaRDI QIDQ2690953

G. G. Braichev

Publication date: 17 March 2023

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Taylor coefficientsupper and lower types of an entire functionzero sequence densities

Mathematics Subject Classification ID

Series expansions of functions of one complex variable (30Bxx) Geometric function theory (30Cxx) Entire and meromorphic functions of one complex variable, and related topics (30Dxx)

Cites Work

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• Development of the Valiron-Levin theorem on the least possible type of entire functions with a given upper \(\rho\)-density of roots
• Zero sequences of holomorphic functions, representation of meromorphic functions. II. Entire functions
• The least type of an entire function of order $ \rho\in(0,1)$ having positive zeros with prescribed averaged densities
• Joint estimates for zeros and Taylor coefficients of entire function
• The exact bounds of lower type magnitude for entire function of order $\rho\in(0,1)$ with zeros of prescribed average densities
• On the least possible type of entire functions of order $ \rho\in(0,1)$ with positive zeros

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