Title PROXIMATE ORDERS AND GENERALIZED INDICATORS OF ENTIRE FUNCTIONS Abstract approved Redacted for Privacy

(Major professor) Frequently, in the theory of entire functions, one is con-fronted with the problem of comparing the growth of two functions f(z) and g(z) as the independent variable z tends to infinity. A well-known procedure for measuring the growth of an entire func-tion f(z) consists of defining the order p of f(z) by p = lim log log M(r) log r r 00 M(r) = max I f(z