Geodesic
On the Connection between the Growth of Zeros and the Decrease of Taylor Coefficients of Entire Functions
Matematičeskie zametki, Tome 113 (2023) no. 1, pp. 32-45

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In the theory of growth of entire functions, two trends have historically developed. The first trend deals with the calculation or estimation of the growth characteristics of the maximum modulus of an entire function (order, type, etc.) in terms of its Taylor series coefficients. In the second trend, the dependence of the growth of a function on the distribution of its zeros is studied. The aim of the present paper is to consider direct connections between the zeros and Taylor coefficients of an entire function, considering both classical and recent advances in the topic.
Keywords: upper and lower types of an entire function, zero sequence densities
Mots-clés : Taylor coefficients. 
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     author = {G. G. Braichev},
     title = {On the {Connection} between the {Growth} of {Zeros} and the {Decrease} of {Taylor} {Coefficients} of {Entire} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {1},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_1_a3/}
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G. G. Braichev. On the Connection between the Growth of Zeros and the Decrease of Taylor Coefficients of Entire Functions. Matematičeskie zametki, Tome 113 (2023) no. 1, pp. 32-45. http://geodesic.mathdoc.fr/item/MZM_2023_113_1_a3/