Geodesic
A refinement of Gol'dberg's theorem on estimating the type with respect to a proximate order of an entire function of integer order
Sbornik. Mathematics, Tome 206 (2015) no. 12, pp. 1771-1796 Cet article a éte moissonné depuis la source Math-Net.Ru

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A best possible second term is found in Gol'dberg's theorem on an asymptotic upper estimate for the logarithm of the maximum modulus of an entire function of integer order. Bibliography: 9 titles.
Keywords: entire function of integer order, type of an entire function with respect to a proximate order, slowly varying function, asymptotic estimate. 
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F. S. Myshakov; A. Yu. Popov. A refinement of Gol'dberg's theorem on estimating the type with respect to a proximate order of an entire function of integer order. Sbornik. Mathematics, Tome 206 (2015) no. 12, pp. 1771-1796. http://geodesic.mathdoc.fr/item/SM_2015_206_12_a5/

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[2] 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 | DOI | MR | Zbl

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[5] A. A. Gol'dberg, “An integral with respect to a semiadditive measure and its application to the theory of entire functions. III”, Amer. Math. Soc. Transl. Ser. 2, 88, Amer. Math. Soc., Providence, R.I., 1970, 181–232 | MR | Zbl

[6] 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”, Sb. Math., 204:5 (2013), 683–725 | DOI | DOI | MR | Zbl

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[8] E. Seneta, Regularly varying functions, Lecture Notes in Math., 508, Springer-Verlag, Berlin–New York, 1976, v+112 pp. | DOI | MR | MR | Zbl | Zbl

[9] S. Saks, Theory of the integral, Monogr. Mat., 7, 2nd ed., G. E. Stechert, Warszawa–New York, 1937, vi+347 pp. | MR | Zbl