# 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 |
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Form | electronic; electronic resource; remote |

Extent | 1 online resource. |

Publication date | 2014 |

Issuance | monographic |

Language | English |

## Creators/Contributors

Associated with | Ha, Junsoo |
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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 |
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## Bibliographic information

Statement of responsibility | Junsoo Ha. |
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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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