Bounded nonvanishing functions and bateman functions
نویسندگان
چکیده
منابع مشابه
Bounded Nonvanishing Functions and Bateman Functions
We consider the family B̃ of bounded nonvanishing analytic functions f(z) = a0 + a1 z + a2 z 2 + · · · in the unit disk. The coefficient problem had been extensively investigated (see e. g. [2], [13], [14], [16], [17], [18], [20]), and it is known that |an| ≤ 2 e for n = 1, 2, 3, and 4. That this inequality may hold for n ∈ IN, is known as the Krzyż conjecture. It turns out that for f ∈ B̃ with a...
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The class S of functions g(z) = z + c 2 z 2 + c 3 z 3 + ... analytic and univalent in the unit disk Izr < 1 has been thoroughly studied, and its properties are well known. Our purpose is to investigate another class of functions which, by contrast, seems to have been rather neglected. This is the class S o of functions f ( z ) = 1 + a 1 z + a 2 z Z + . . , analytic, univalent, and nonvanishing ...
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In this article we prove that given a holomorphic cusp form f and any point s0 in the complex plane, there is a holomorphic cusp form g such that the Rankin-Selberg L-function L(s, f × g) is non-zero at s0. Résumé: Dans cet article, on prouve le résultat suivant. Etat donné une forme holomorphe cuspidale f et un point quelquonque du plan complexe, il existe une forme holomorphe cuspidale g tell...
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S O u {1} is a compact subset of A. Duren and Schober had been interested in extreme points and support points of S o. Recall that a support point of a family F is a function which maximizes the real part of some continuous linear functional, that is not constant over F. We shall give a characterization of the extreme points and support points of the subfamily So(R ) of nonvanishing univalent f...
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ژورنال
عنوان ژورنال: Complex Variables, Theory and Application: An International Journal
سال: 1994
ISSN: 0278-1077,1563-5066
DOI: 10.1080/17476939408814746