Geodesic
The most rapid possible growth of the maximum modulus of a~canonical product of noninteger order with a~prescribed majorant of the counting function of zeros
Sbornik. Mathematics, Tome 204 (2013) no. 5, pp. 683-725

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Asymptotically sharp estimates for the logarithm of the maximum modulus of a canonical product are obtained in the case when the counting function of zeros has a prescribed majorant, while the arguments of the zeros can be arbitrary. Bibliography: 9 titles.
Keywords: entire function of finite order, proximate order, canonical product, maximum modulus of an entire function. 
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     title = {The most rapid possible growth of the maximum modulus of a~canonical product of noninteger order with a~prescribed majorant of the counting function of zeros},
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A. Yu. Popov. The most rapid possible growth of the maximum modulus of a~canonical product of noninteger order with a~prescribed majorant of the counting function of zeros. Sbornik. Mathematics, Tome 204 (2013) no. 5, pp. 683-725. http://geodesic.mathdoc.fr/item/SM_2013_204_5_a3/