Upper bounds and moments of L-functions
Abstract/Contents
- Abstract
- L-functions are some of the most studied objects in number theory. Although many crucial properties of L-functions remain mysterious, central conjectures such as the generalized Riemann hypothesis (GRH). This thesis concerns properties of L-functions. In particular, we focus on studying upper bounds and moments of $L$-functions. Assuming GRH, we give effective explicit upper bounds for L-functions on the critical line and apply these bounds to determine what numbers are represented by a given ternary quadratic form. Moreover the best known version of the Lindelof hypothesis from the Riemann hypothesis (RH) is also derived. Another important way of understanding LH is through moments of L-functions. Information about moments sheds light on the distribution of values of \zeta(1/2 + it). We try to understand the joint distribution of quantities like \zeta(1/2 + it) and \zeta(1/2 + it + i). To study these we consider "shifted moments" of the zeta function and obtain good upper and lower estimates for such moments.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2010 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Chandee, Vorrapan |
|---|---|
| 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 |
|---|
Bibliographic information
| Statement of responsibility | Vorrapan Chandee. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2010. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2010 by Vorrapan Chandee
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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