# Distribution problems in number theory

## Abstract/Contents

- Abstract
- Four separate problems are considered. The first chapter concerns the average equidistribution of Heegner points attached to elements of fixed order in the class group of imaginary quadratic fields. Some discussion of the Cohen-Lenstra heuristics is also included. Chapter 2 treats the distribution of the logarithm of two families of L-functions at the central point. The most easily stated consequence is that the central values of L-functions attached to modular forms of large weight converge to 0 in distribution as the weight tends to infinity. Chapter 3 concerns omega results for large sums of Dirichlet characters. The length N of the sum is treated as a parameter that is allowed to vary with the modulus q of the characters. For N small compared to q the large values exhibited are related to the distribution of smooth numbers, while for larger N the results are analogous to omega bounds known for the corresponding L-functions. The final chapter gives a mixing time analysis for the random k-cycle walk on the symmetric group. The main new analytic ingredient is an asymptotic formula for many character ratios evaluated at a k-cycle.

## Description

Type of resource | text |
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Form | electronic; electronic resource; remote |

Extent | 1 online resource. |

Publication date | 2012 |

Issuance | monographic |

Language | English |

## Creators/Contributors

Associated with | Hough, Robert Daniel | |
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Associated with | Stanford University, Department of Mathematics | |

Primary advisor | Soundararajan, Kannan, 1973- | |

Thesis advisor | Soundararajan, Kannan, 1973- | |

Thesis advisor | Diaconis, Persi | |

Thesis advisor | Venkatesh, Akshay, 1981- | |

Advisor | Diaconis, Persi | |

Advisor | Venkatesh, Akshay, 1981- |

## Subjects

Genre | Theses |
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## Bibliographic information

Statement of responsibility | Robert Hough. |
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Note | Submitted to the Department of Mathematics. |

Thesis | Thesis (Ph.D.)--Stanford University, 2012. |

Location | electronic resource |

## Access conditions

- Copyright
- © 2012 by Robert Daniel Hough
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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