Introduction to Value Distribution Theory of Meromorphic Maps

1982 ◽  
pp. 210-359 ◽  
Author(s):  
Wilhelm Stoll
Keyword(s):  
Distribution Theory ◽  
Value Distribution ◽  
Value Distribution Theory ◽  
Meromorphic Maps

scholarly journals Uniqueness problem with truncated multiplicities in value distribution theory

1998 ◽  
Vol 152 ◽  
pp. 131-152 ◽  
Author(s):  
Hirotaka Fujimoto
Keyword(s):  
General Position ◽  
Meromorphic Functions ◽  
Distribution Theory ◽  
Value Distribution ◽  
Uniqueness Problem ◽  
Value Distribution Theory ◽  
Meromorphic Maps

Abstract.In 1929, H. Cartan declared that there are at most two meromorphic functions on ℂ which share four values without multiplicities, which is incorrect but affirmative if they share four values counted with multiplicities truncated by two. In this paper, we generalize such a restricted H. Cartan’s declaration to the case of maps into PN (ℂ). We show that there are at most two nondegenerate meromorphic maps of ℂn into PN(ℂ) which share 3N + 1 hyperplanes in general position counted with multiplicities truncated by two. We also give some degeneracy theorems of meromorphic maps into PN (ℂ) and discuss some other related subjects.

scholarly journals Uniqueness problem with truncated multiplicities in value distribution theory, II

1999 ◽  
Vol 155 ◽  
pp. 161-188 ◽  
Author(s):  
Hirotaka Fujimoto
Keyword(s):  
General Position ◽  
Distribution Theory ◽  
Value Distribution ◽  
Uniqueness Problem ◽  
Value Distribution Theory ◽  
Meromorphic Maps

AbstractLet H1, H2,…,Hq be hyperplanes in PN (ℂ) in general position. Previously, the author proved that, in the case where q ≥ 2N + 3, the condition ν(f,Hj) = ν(g, Hj) imply f = g for algebraically nondegenerate meromorphic maps f, g: ℂn → PN(ℂ), where ν(f, Hj) denote the pull-backs of Hj through f considered as divisors. In this connection, it is shown that, for q ≥ 2N + 2, there is some integer ℓ0 such that, for any two nondegenerate meromorphic maps f, g: ℂn → PN(ℂ) with min(ν(f, Hj),ℓ0) = min(ν(g, Hj), ℓ0) the map f × g into PN(ℂ) × PN(ℂ) is algebraically degenerate. He also shows that, for N = 2 and q = 7, there is some ℓ0 such that the conditions min(ν(f, Hj), ℓ0) = min(ν(g, Hj), ℓ0) imply f = g for any two nondegenerate meromorphic maps f, g into P2(ℂ) and seven generic hyperplanes Hj’s.

On the value distribution theory of elliptic functions

1984 ◽  
Vol 98 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Steven B. Bank ◽  
J. K. Langley
Keyword(s):  
Elliptic Functions ◽  
Distribution Theory ◽  
Value Distribution ◽  
Value Distribution Theory

scholarly journals Riemann Hypothesis and Value Distribution Theory

2017 ◽  
Vol 05 (03) ◽  
pp. 734-740
Author(s):  
Jinhua Fei
Keyword(s):  
Riemann Hypothesis ◽  
Distribution Theory ◽  
Value Distribution ◽  
Value Distribution Theory
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