Title:
Problems in combinatorial number theory

Thumbnail Image
Author(s)
Amirkhanyan, Gagik M.
Authors
Advisor(s)
Wick, Brett D.
Advisor(s)
Editor(s)
Associated Organization(s)
Organizational Unit
Organizational Unit
Series
Supplementary to
Abstract
The dissertation consists of two parts. The first part is devoted to results in Discrepancy Theory. We consider geometric discrepancy in higher dimensions (d > 2) and obtain estimates in Exponential Orlicz Spaces. We establish a series of dichotomy-type results for the discrepancy function which state that if the L¹ norm of the discrepancy function is too small (smaller than the conjectural bound), then the discrepancy function has to be very large in some other function space.The second part of the thesis is devoted to results in Additive Combinatorics. For a set with small doubling an order-preserving Freiman 2-isomorphism is constructed which maps the set to a dense subset of an interval. We also present several applications.
Sponsor
Date Issued
2014-04-02
Extent
Resource Type
Text
Resource Subtype
Dissertation
Rights Statement
Rights URI