Sums of Polynomials, Minmax Problems and Number Theory
Kim, Seon-Hong
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https://hdl.handle.net/2142/86990
Description
Title
Sums of Polynomials, Minmax Problems and Number Theory
Author(s)
Kim, Seon-Hong
Issue Date
2000
Doctoral Committee Chair(s)
Stolarsky, K.B.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
The study in the second direction is to formulate a new fundamental method to solve some extremal problems. We study certain minmax problems about unit vectors in the plane that are best formulated in terms of complex exponentials. We transform these problems into problems about determining whether certain collections of planar convex sets are packings. This new method is successfully applied to other extremal problems. Moreover we study some minmax problems for fractional parts of real numbers.
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