Accession Number : AD0267853

Title :   Meromorphic Functions with Two Values Distributed on a finite Number of Paths Extending to Infinity,

Corporate Author : SYRACUSE UNIV N Y

Personal Author(s) : EDREI,ALBERT

Report Date : MAY 1961

Pagination or Media Count : 1

Abstract : Let f(z) be a meromorphic function such that all its zeros and poles lie on a finite number of regular, separated paths extending to infinity. (The exact definitions of regular and separated are defined.) It is shown that if T(T does not equal zero, T does not equal infinity) is a deficient value (in the sense of Nevanlinna0 of f(z), or of any one of its derivatives, there must exist severe restrictions on the order Lambda of f(z). In fact, Lambda must be finite and cannot exceed a bound depending only on the configuration of the paths carrying the zeros and poles of f(z). This shows that, if three distinct values, finite or infinite, are distributed on a finite number of paths and if the order of f(z) is infinite, or finite but large enough, then no value, finite or infinite, may be deficient. In particular, entire functions of infinite order cannot have two finite values distributed on a finite number of regular, separated paths. (Author)

Descriptors :   BESSEL FUNCTIONS, COMPLEX VARIABLES, DIFFERENTIAL EQUATIONS, FUNCTIONS(MATHEMATICS), INEQUALITIES, INTEGRAL TRANSFORMS, NUMERICAL INTEGRATION, MEASURE THEORY, POLYNOMIALS

Distribution Statement : APPROVED FOR PUBLIC RELEASE