Diophantine generation, Galois theory, and Hilbert's tenth problem / by Kendra Kennedy.
| Author/creator | Kennedy, Kendra |
| Other author | Shlapentokh, Alexandra. |
| Other author | East Carolina University. Department of Mathematics. |
| Format | Theses and dissertations |
| Publication Info | [Greenville, N.C.] : East Carolina University, 2012. |
| Description | 58 pages : digital, PDF file |
| Supplemental Content | Access via ScholarShip |
| Subjects |
| Summary | Hilbert's Tenth Problem was a question concerning existence of an algorithm to determine if there were integer solutions to arbitrary polynomial equations over the integers. Building on the work by Martin Davis, Hilary Putnam, and Julia Robinson, in 1970 Yuri Matiyasevich showed that such an algorithm does not exist. One can ask a similar question about polynomial equations with coefficients and solutions in the rings of algebraic integers. In this thesis, we survey some recent developments concerning this extension of Hilbert's Tenth Problem. In particular we discuss how properties of Diophantine generation and Galois Theory combined with recent results of Bjorn Poonen, Barry Mazur, and Karl Rubin show that the Shafarevich-Tate conjecture implies that there is a negative answer to the extension of Hilbert's Tenth Problem to the rings of integers of number fields. |
| General note | Presented to the faculty of the Department of Mathematics. |
| General note | Advisor: Alexandra Shlapentokh. |
| General note | Title from PDF t.p. (viewed July 2, 2012). |
| Dissertation note | M.A. East Carolina University 2012. |
| Bibliography note | Includes bibliographical references. |
| Technical details | System requirements: Adobe Reader. |
| Technical details | Mode of access: World Wide Web. |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | Access Content Online | ✔ Available |