On the growth rate of composite meromorphic functions

Abstract

Let f be a meromorphic function and let T(r.f) be its Nevanlinna characteristic. Let g be an entire function of non-zero order p(g) and suppose that 0 < μ < p(g). It is proved that . Some applications are given. It is shown that certain results by Gross and Yang, Schönhage, Singh and others on the growth rate of composite entire function hold for meromorphic functions as well. Other applications concern the functional equation f(h(z))=f(k(z)) and analytic mappings between ultrahyperelliptic surfaces. This improves results by Niino.

AMS No.:

• 30D05

^*Research performed as a feodor lynen research fellow of the alexander von humboldt foundation at cornell university

^*Research performed as a feodor lynen research fellow of the alexander von humboldt foundation at cornell university

Notes

^*Research performed as a feodor lynen research fellow of the alexander von humboldt foundation at cornell university