On the maximum modulus principle for the tangential Cauchy-Riemann equations

1974 ◽  
Vol 208 (2) ◽  
pp. 91-97 ◽  
Author(s):  
James A. Carlson ◽  
C. Denson Hill
Keyword(s):  
Maximum Modulus ◽  
Maximum Modulus Principle ◽  
Cauchy Riemann

scholarly journals The local maximum modulus principle for function spaces

1975 ◽  
Vol 51 (2) ◽  
pp. 109-112
Author(s):  
Yukio Hirashita ◽  
Junzo Wada
Keyword(s):  
Local Maximum ◽  
Maximum Modulus ◽  
Function Spaces ◽  
Maximum Modulus Principle

Linear forms in algebraic points of Abelian functions. II

1976 ◽  
Vol 79 (1) ◽  
pp. 55-70 ◽  
Author(s):  
D. W. Masser
Keyword(s):  
Analytic Function ◽  
Maximum Modulus ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Maximum Modulus Principle ◽  
Linear Forms ◽  
Extrapolation Procedure ◽  
Abelian Functions

In this paper we continue to develop the apparatus needed for the proof of the theorem announced in (11). We retain the notation of (11) together with the assumptions made there about the field of Abelian functions. This section deals with properties of more general functions holomorphic on Cn. When n = 1 the extrapolation procedure in problems of transcendence is essentially the maximum modulus principle together with the act of dividing out zeros of an analytic function. For n > 1, however, this approach is not possible, and some mild theory of several complex variables is required. This was first used in the context of transcendence by Bombieri and Lang in (2) and (12), and we now give a brief account of the basic constructions of their papers.

Sign in / Sign up

Export Citation Format

Share Document