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Title:  Waring's Problem for Linear Polynomials and Laurent Polynomials 
Author(s):  Kim, DongIl 
Doctoral Committee Chair(s):  Aimo Hinkkanen 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Mathematics 
Abstract:  Waring's problem is about representing any function in a class of functions as a sum of kth powers of nonconstant functions in the same class. We allow complex coefficients in these kind of problems. Consider i=1p1 fiz k=z and i=1p1 fizk =1 . For a given k ≥ 2, let p 1 and p2 be the smallest numbers of functions that give the above identities. W. K. Hayman obtained lower bounds of p1 and p2 for polynomials, entire functions, rational functions and meromorphic functions. First, we consider Waring's problem for linear polynomials and get p 1 = k and p2 ≥ k + 1. Next, we study Waring's problem for Laurent polynomials and obtain lower bounds of p1 and p 2. Finally, we discuss the misquote that I discovered in the proof of Hayman's theorem. 
Issue Date:  2003 
Type:  Text 
Language:  English 
Description:  52 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 2003. 
URI:  http://hdl.handle.net/2142/86812 
Other Identifier(s):  (MiAaPQ)AAI3086095 
Date Available in IDEALS:  20150928 
Date Deposited:  2003 
This item appears in the following Collection(s)

Dissertations and Theses  Mathematics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois