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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] B. Ja. Levin, Distribution of zeros of entire functions, Amer. Math. Soc., Providence, RI, 1964 | MR | MR | Zbl | Zbl

[2] G. Valiron, Lectures on the general theory of integral functions, Deighton, Bell, Cambridge, 1923 | Zbl

[3] J. Hadamard, “Essai sur l'etude des fonctions données par leur développement de Taylor”, Jour. de Math. Ser. 4, 8 (1982), 101–186 | Zbl

[4] G. Valiron, “Sur les fonctions entières d'ordre nul et d'ordre fini et en particulier les fonctions à correspondance régulière”, Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys. (3), 5 (1913), 117–257 | MR | Zbl

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[6] A. Denjoy, “Sur les produits canoniques d'ordre infini”, Journ. de Math. (6), 6 (1910), 1–136 | Zbl

[7] G. Pólya, G. Szegö, Aufgaben und Lehrsätze aus der Analysis, v. I, Springer-Verlag, Berlin–New York, 1964 | MR | MR | Zbl

[8] A. Erdélyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of integral transforms, vol. I, McGraw-Hill, New York–Toronto–London, 1954 | MR | MR | Zbl | Zbl

[9] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integrals and series. Vol. 1. Elementary functions, Gordon Breach, New York, 1986 | MR | MR | Zbl | Zbl