# Value distribution of automorphic forms in a family

## Abstract/Contents

- Abstract
- Consider the modular surface $X = SL_2(\BZ) \backslash \BH$. One would like to know how the values of holomorphic modular forms/non-holomorphic Maass forms would distribute in the limit. Hejhal and Rackner \cite{HejRac} was the first people to study this problem. They conjectured that (suitably normalized) Maass forms suitably normalized would distribute like the Gaussian with mean 0 and variance $\frac{3}{\pi}$ in the limit. This is known as the random wave conjecture. They also gave a heuristic argument on why the conjecture should hold. This thesis tries to address two questions centered around the random wave conjecture and related problems, such as Quantum Unique Ergodicity. The first part of the thesis (Chapter 3) addresses the discrepancy of predictions by physicists and by mathematicians. For a fixed test function on $X$, Quantum Unique Ergodicity asserts that $$\mu_j (\psi) := \int_X \psi(z)

## Description

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

Extent | 1 online resource. |

Publication date | 2016 |

Issuance | monographic |

Language | English |

## Creators/Contributors

Associated with | Siu, Ho Chung |
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Associated with | Stanford University, Department of Mathematics. |

Primary advisor | Soundararajan, Kannan, 1973- |

Thesis advisor | Soundararajan, Kannan, 1973- |

Thesis advisor | Bump, Daniel, 1952- |

Thesis advisor | Venkatesh, Akshay, 1981- |

Advisor | Bump, Daniel, 1952- |

Advisor | Venkatesh, Akshay, 1981- |

## Subjects

Genre | Theses |
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## Bibliographic information

Statement of responsibility | Ho Chung Siu. |
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Note | Submitted to the Department of Mathematics. |

Thesis | Thesis (Ph.D.)--Stanford University, 2016. |

Location | electronic resource |

## Access conditions

- Copyright
- © 2016 by Ho Chung Siu
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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