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Aimo Hinkkanen Kim, Dong-Il 2015-09-28T15:19:39Z 2015-09-28T15:19:39Z 10000-01-01 2003 2003 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. Made available in DSpace on 2015-09-28T15:19:39Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3086095.pdf: 1883591 bytes, checksum: 50a60b280531d3b94a80505beecbca97 (MD5) Previous issue date: 2003 Embargo set by: Seth Robbins for item 88093 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 52 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003. http://hdl.handle.net/2142/86812 (MiAaPQ)AAI3086095 eng Mathematics Waring's Problem for Linear Polynomials and Laurent Polynomials text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.