Sums of singular series and the distribution of primes
Abstract/Contents
- Abstract
- The Hardy--Littlewood k-tuples conjectures generalize the twin primes conjecture by predicting the asymptotic number of twin primes less than a real number x; they go even further by predicting the number of times that any specific configuration appears in the primes, and involve important constants known as the singular series constants. The Hardy--Littlewood conjectures arise in many computations concerning the distribution of primes, including the distribution of primes in short intervals and its moments and the distribution of prime gaps. Correspondingly, understanding various sums of singular series is crucial to understanding many aspects of the distribution of primes. For example, Montgomery and Soundararajan computed the distribution of primes in short intervals by estimating lower-order terms of certain sums of singular series. We explore various refinements and generalizations of known results on sums of singular series, including better estimates for sums over sets of size k when k is odd, averages over configurations that are restricted to certain arithmetic progressions, estimates when k is large with respect to the range of the sum, and function field analogs.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2022; ©2022 |
| Publication date | 2022; 2022 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Kuperberg, Vivian Zieve |
|---|---|
| Degree supervisor | Soundararajan, Kannan, 1973- |
| Thesis advisor | Soundararajan, Kannan, 1973- |
| Thesis advisor | Bump, Daniel, 1952- |
| Thesis advisor | Fox, Jacob, 1984- |
| Degree committee member | Bump, Daniel, 1952- |
| Degree committee member | Fox, Jacob, 1984- |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Vivian Kuperberg. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2022. |
| Location | https://purl.stanford.edu/mz553sv1729 |
Access conditions
- Copyright
- © 2022 by Vivian Zieve Kuperberg
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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