Characteristic, maximum modulus and value distribution

Authors:
W. K. Hayman and J. F. Rossi

Journal:
Trans. Amer. Math. Soc. **284** (1984), 651-664

MSC:
Primary 30D35; Secondary 30D20

MathSciNet review:
743737

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Abstract: Let be an entire function such that on a set of positive upper density. Then has no finite deficient values. In fact, if we assume that has density one and has nonzero order, then the roots of all equations are equidistributed in angles. In view of a recent result of Murai [**6**] the conclusions hold in particular for entire functions with Fejér gaps.

**[1]**Albert Edrei and Wolfgang H. J. Fuchs,*Bounds for the number of deficient values of certain classes of meromorphic functions*, Proc. London Math. Soc. (3)**12**(1962), 315–344. MR**0138765****[2]**W. K. Hayman,*The minimum modulus of large integral functions*, Proc. London Math. Soc. (3)**2**(1952), 469–512. MR**0056083****[3]**W. K. Hayman,*Angular value distribution of power series with gaps*, Proc. London Math. Soc. (3)**24**(1972), 590–624. MR**0306497****[4]**W. K. Hayman,*On Iversen’s theorem for meromorphic functions with few poles*, Acta Math.**141**(1978), no. 1-2, 115–145. MR**0492265****[5]**W. K. Hayman and F. M. Stewart,*Real inequalities with applications to function theory*, Proc. Cambridge Philos. Soc.**50**(1954), 250–260. MR**0061638****[6]**Takafumi Murai,*The deficiency of entire functions with Fejér gaps*, Ann. Inst. Fourier (Grenoble)**33**(1983), no. 3, 39–58 (English, with French summary). MR**723947**

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DOI:
https://doi.org/10.1090/S0002-9947-1984-0743737-2

Article copyright:
© Copyright 1984
American Mathematical Society