

Title of Thesis
Algebraic Properties of Entire Functions with Coefficients in
Particular Valued Fields 
Author(s)
SARDAR MOHIB
ALI KHAN 
Institute/University/Department
Details Abdus Salam School of Mathematical Sciences / GC
University, Lahore 
Session 2010 
Subject Mathematics 
Number of Pages 86 
Keywords (Extracted from title, table of contents and
abstract of thesis) Algebraic, Properties, Entire,
Functions, Coefficients, Particular, Valued Fields, Polya,
polynomials, function theory 
Abstract The study of entire
functions is of central importance in complex function theory. We
consider the ring of entire functions either on sub fields of C or
on some sub fields of Cp: By using a technique based on admissible
filters we study the ideal structure of the ring of entire
functions. Then we prove the B ezout property for the ring of entire
functions over Cp independent of MittagLe er theorem.
An important problem in complex function theory is to find an entire
function from its values on a given sequence. By means of socalled
Newton entire functions we solve a series of interpolation problems.
Then we obtain a general result which implies the results of Polya
and Gel'fond on the entire functions which are polynomials. We prove
a similar result for the entire functions f such that f(D) D; where
D is a particular bounded set. As an application we replace the use
of power series for the initial value problems for ODE's with Newton
series for boundary value problems.

