A spread relation for entire functions with negative zeros

Author:
Faruk F. Abi-Khuzam

Journal:
Proc. Amer. Math. Soc. **110** (1990), 951-960

MSC:
Primary 30D35

MathSciNet review:
1028282

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Abstract: Let be a canonical product having only real negative zeros and nonintegral order , and let be the set function defined by . It is shown that if is the set of values of where is a sequence of Polya peaks of and is the deficiency of the value zero of then . This inequality leads to a sharp spread relation for .

**[1]**Faruk F. Abi-Khuzam,*An Abelian theorem for a class of subharmonic functions*, Proc. Amer. Math. Soc.**67**(1977), no. 2, 253–259. MR**0460667**, 10.1090/S0002-9939-1977-0460667-6**[2]**Faruk F. Abi-Khuzam,*The order of entire functions with radially distributed zeros*, Proc. Amer. Math. Soc.**82**(1981), no. 1, 71–75. MR**603604**, 10.1090/S0002-9939-1981-0603604-4**[3]**Albert Baernstein II,*Proof of Edrei’s spread conjecture*, Proc. London Math. Soc. (3)**26**(1973), 418–434. MR**0374429****[4]**Albert Edrei,*The deficiencies of meromorphic functions of finite lower order*, Duke Math. J.**31**(1964), 1–21. MR**0158079****[5]**Simon Hellerstein and Jack Williamson,*Entire functions with negative zeros and a problem of R. Nevanlinna.*, J. Analyse Math.**22**(1969), 233–267. MR**0247087**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1990-1028282-X

Article copyright:
© Copyright 1990
American Mathematical Society