Explorations of sum-product phenomena in fields
by Shen, Chun-Yen, Ph.D., INDIANA UNIVERSITY, 2010, 82 pages; 3409788

Abstract:

We study the sum-product phenomena in finite fields and in reals. The well known sum-product theorem says that under certain circumstances it is not possible for a set to have both an additive and a multiplicative structure. In this dissertation, we first study a quantitative version of the sum-product theorem, and give a stronger sum-product theorem in general fields. We also use Fourier analytic machinery to investigate the expanding property of a family of two variables polynomials. We then use Fourier analytic methods to characterize the polynomials such that when a set behaves like an arithmetic progression, then the size of its image under the polynomials is large. We also study the Erdös-Falconer distance problems in vector space over finite fields. Some analogous results in real setting are also derived.

 
AdviserNets Katz
SchoolINDIANA UNIVERSITY
SourceDAI/B 71-07, p. , Aug 2010
Source TypeDissertation
SubjectsMathematics
Publication Number3409788
Adobe PDF Access the complete dissertation:
 

» Find an electronic copy at your library.
  Use the link below to access a full citation record of this graduate work:
  http://gateway.proquest.com/openurl%3furl_ver=Z39.88-2004%26res_dat=xri:pqdiss%26rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation%26rft_dat=xri:pqdiss:3409788
  If your library subscribes to the ProQuest Dissertations & Theses (PQDT) database, you may be entitled to a free electronic version of this graduate work. If not, you will have the option to purchase one, and access a 24 page preview for free (if available).

About ProQuest Dissertations & Theses
With over 2.3 million records, the ProQuest Dissertations & Theses (PQDT) database is the most comprehensive collection of dissertations and theses in the world. It is the database of record for graduate research.

The database includes citations of graduate works ranging from the first U.S. dissertation, accepted in 1861, to those accepted as recently as last semester. Of the 2.3 million graduate works included in the database, ProQuest offers more than 1.9 million in full text formats. Of those, over 860,000 are available in PDF format. More than 60,000 dissertations and theses are added to the database each year.

If you have questions, please feel free to visit the ProQuest Web site - http://www.proquest.com - or call ProQuest Hotline Customer Support at 1-800-521-3042.