Some problems in multiplicative number theory
Abstract/Contents
- Abstract
- Let q be a power of a prime p. In the first part of this thesis, we establish the upper bound of the least prime primitive root mod q by p^3.1. We say a polynomial in F_q [T] is m-smooth if all of its irreducible factors are of degree less than or equal to m. Let N(n, m) be the number of solutions to the polynomial equation X+Y=2Z where all variables are m-smooth polynomials of degree n. In the second part of this thesis, we establish a lower bound on N(n, m) when (8+d) log_q n < = m < = n^1/2 for small d, and prove the analog of the xyz conjecture of Lagarias and Soundararajan in the polynomial rings over finite fields.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2014 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Ha, Junsoo |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Soundararajan, Kannan, 1973- |
| Thesis advisor | Soundararajan, Kannan, 1973- |
| Thesis advisor | Conrad, Brian, 1970- |
| Thesis advisor | Venkatesh, Akshay, 1981- |
| Advisor | Conrad, Brian, 1970- |
| Advisor | Venkatesh, Akshay, 1981- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Junsoo Ha. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2014. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2014 by Junsoo Ha
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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