A remark on Schottky's theorem

2007 ◽  
Vol 39 (2) ◽  
pp. 242-246 ◽  
Author(s):  
Zhong Li ◽  
Yi Qi
Keyword(s):  
Schottky’S Theorem

Some remarks on Schottky's theorem

1947 ◽  
Vol 43 (4) ◽  
pp. 442-454 ◽  
Author(s):  
W. K. Hayman
Keyword(s):  
Schottky’S Theorem ◽  
Image Position

1. We denote by the class of all functions regular in |z| < 1, and never taking the values 0 or 1 in |z| < 1. Then Schottky's(1) theorem states:Theorem A. Let f(z) = a0 + a1z + … belong to . Thenand hencewhereand the constantsK(a0), K(a0,ρ) depend only on the quantities indicated.

scholarly journals On Explicit Bounds In Schottky's Theorem

1955 ◽  
Vol 7 ◽  
pp. 76-82 ◽  
Author(s):  
J. A. Jenkins
Keyword(s):  
Explicit Estimate ◽  
Absolute Value ◽  
Schottky’S Theorem ◽  
Explicit Bounds

1. Introduction. To Schottky is due the theorem which states that a function F(Z), regular and not taking the values 0 and 1 in |Z| < 1 and for which F(0) = a0, is bounded in absolute value in |Z| ≤ r, 0 ≤ r < 1, by a number depending only on a0 and r. Let K(a0 r) denote the best possible bound in this result. Various authors have dealt with the problem of giving an explicit estimate for this bound.

On Explicit Bounds in Landau's Theorem. II

1981 ◽  
Vol 33 (3) ◽  
pp. 559-562 ◽  
Author(s):  
James A. Jenkins
Keyword(s):  
Taylor Expansion ◽  
Slight Modification ◽  
Schottky’S Theorem ◽  
Explicit Bounds ◽  
Image Position ◽  
Explicit Expressions

Quite some years ago a number of mathematicians were interested in obtaining explicit expressions for the bounds in Schottky's and Landau's theorems, specifically numerically évaluable bounds of a particular form. The best bounds of this type in Schottky's theorem were given by the author [3]. For Landau's theorem the chosen form is as follows. Let F(Z) be regular in |Z| < 1, omit the values 0 and 1 and have Taylor expansion about Z = 0ThenUsing the same method employed for Schottky's theorem the author showed that one can take K = 5.94. By a slight modification of the author's method Lai [6] gave the further value K = 4.76.

Quantum correction for Schottky's theorem

Physica B+C ◽  
1977 ◽  
Vol 90 (2) ◽  
pp. 262-264 ◽  
Author(s):  
A. van der Ziel
Keyword(s):  
Quantum Correction ◽  
Schottky’S Theorem
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