Moments and zeros of L-functions over function fields
Abstract/Contents
- Abstract
- In this thesis we study some questions related to L-functions over function fields. We obtain asymptotic formulas for the first four moments of the family of quadratic Dirichlet L-functions, when the size of the finite field is fixed and the genus goes to infinity. For the first moment we also compute an explicit lower order term of size approximately the cube root of the main term. In joint work with Hung Bui, we study low-lying zeros in the same family of L-functions. For the one-level density of zeros, we detect a lower order term when the support of the Fourier transform of the test function is sufficiently restricted. We also compute the pair correlation of zeros and obtain a non-vanishing result and a lower bound for the proportion of simple zeros in the family.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2017 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Florea, Alexandra Mihaela |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Soundararajan, Kannan, 1973- |
| Thesis advisor | Soundararajan, Kannan, 1973- |
| Thesis advisor | Conrad, Brian |
| Thesis advisor | Entin, Alexei |
| Thesis advisor | Venkatesh, Akshay, 1981- |
| Advisor | Conrad, Brian |
| Advisor | Entin, Alexei |
| Advisor | Venkatesh, Akshay, 1981- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Alexandra Mihaela Florea. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2017. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2017 by Alexandra Mihaela Florea
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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