Geodesic
On the Lower Indicator of an Entire Function
Matematičeskie zametki, Tome 107 (2020) no. 6, pp. 817-832

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The paper deals with an entire function of noninteger order with a sequence of negative roots having (for this order) zero lower and finite upper densities. Sharp estimates for the lower indicator of such a function are obtained. It is proved that, in some angles, this characteristic is identically zero, and its form in the other angles is obtained provided that the sequence of roots of the entire function sufficiently rapidly tends to infinity.
Keywords: entire function, type and lower type of a function, indicator and lower indicator, upper and lower densities of a set of roots, completely regular growth. 
@article{MZM_2020_107_6_a1,
     author = {G. G. Braichev},
     title = {On the {Lower} {Indicator} of an {Entire} {Function}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {817--832},
     publisher = {mathdoc},
     volume = {107},
     number = {6},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_6_a1/}
}
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G. G. Braichev. On the Lower Indicator of an Entire Function. Matematičeskie zametki, Tome 107 (2020) no. 6, pp. 817-832. http://geodesic.mathdoc.fr/item/MZM_2020_107_6_a1/