Cheng, Jiuyi2014-03-142014-03-141994-01-04etd-06072006-124203http://hdl.handle.net/10919/38553This dissertation investigates two problems in the function theory of one complex variable. In Chapter 1, we study the asymptotics and zero distribution of solutions of the differential equation wⁿ + A(z)w = 0, where A(z) is a transcendental entire function of very slow growth. The result parallels the classical case when A(z) is assumed to be a polynomial. An analogue concerning the case when A(z) is a transcendental entire function whose series expansion satisfies the Hadamard gap condition is given. In Chapter 2, we give upper bounds for the number of deficient functions of entire functions of completely regular growth and entire functions whose zeros have angular densities. In particular, the bound is 2λ + 1 if the entire function is of completely regular growth with order λ, 0 < λ < ∞.vi, 62 leavesBTDapplication/pdfenIn CopyrightLD5655.V856 1994.C546Differential equations -- Numerical solutionsFunctions, EntireDissertationhttp://scholar.lib.vt.edu/theses/available/etd-06072006-124203/