ON PERIODIC LEFT FACTORS OF MEROMORPHIC FUNCTIONS.
Abstract
A study is made of the left factors of mod periodic functions. It is shown that if f(z) is a nonconstant meromorphic function periodic with period beta and if f(p(z)) is periodic modulo an entire function h(z) (p is a polynomial of degree k > 1), then h(z) must be of order = or > k - 1. Furthermore, if f is meromorphic and periodic modulo g(z), rho(g) < k - 1/(k), rho(g) < rho(f), (rho(f) denotes the order of f), and f(p(z)) is periodic mod h, then rho(h) = or > k - 1. This is proved for k = 2, but the result holds in general. Additional results of this type are also established. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 16, 1969
- Accession Number
- AD0695774
Entities
People
- Fred Gross
Organizations
- United States Naval Research Laboratory