On an entire function of an entire function defined by Dirichlet series
نویسندگان
چکیده
منابع مشابه
On Entire Functions Defined by a Dirichlet Series: Correction
1. As pointed out by Sunyer i Balaguer in the preceding paper the proofs of Theorem 1 and of the second part of Theorem 2 of our paper [l ] are faulty. We observe that if we impose the additional hypothesis that Afs(D), is a nonincreasing function for sufficiently small a then the proofs can be made to work. After correction Theorem 1 and the second part of Theore...
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In this paper, we introduce the idea of relative order and type of entire functions represented by Banach valued Dirichlet series of two complex variables to generalize some earlier results. Proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by Dirichlet series is the same as that of i...
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If Piz) is an entire function of order p, it is known that (1) M, m are its type and co-type, in case/ happens to be the rank (or position) function of the maximum term of the Maclaurin series of P (see Chapter II of [l] and Chapter II of [2]) and that (2) M and m are the logarithmic type and co-type of P, if fix) is the number of zeroes z of Piz) such that \z\ ^x (see Jensen's Theorem, Chapter...
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Introduction. In two previous notes [9],1 I stated some results which, in a general way, may be expressed as follows: If the Taylor series which represents an entire function satisfies a certain gap condition (which depends only on the order of F(z)), the zeros of F(z) —f(z) are not exceptional with respect to the proximate order of F(z) by any meromorphic function f(z) ^ w of lower order. On t...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1966
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1966.18.379