Ask a Librarian

Threre are lots of ways to contact a librarian. Choose what works best for you.

HOURS TODAY

Closed

Reference Desk

CONTACT US BY PHONE

(802) 656-2022

Voice

(802) 503-1703

Text

MAKE AN APPOINTMENT OR EMAIL A QUESTION

Schedule an Appointment

Meet with a librarian or subject specialist for in-depth help.

Email a Librarian

Submit a question for reply by e-mail.

WANT TO TALK TO SOMEONE RIGHT AWAY?

Library Hours for Saturday, November 18th

All of the hours for today can be found below. We look forward to seeing you in the library.
HOURS TODAY
Closed
MAIN LIBRARY

SEE ALL LIBRARY HOURS
WITHIN BAILEY/HOWE

MapsClosed

Media ServicesClosed

Reference DeskClosed

Cyber Cafe (All Night Study)Closed

OTHER DEPARTMENTS

Special CollectionsClosed

Dana Medical Library9:00 am - 8:00 pm

Classroom Technology ServicesClosed

 

CATQuest

Search the UVM Libraries' collections

UVM Theses and Dissertations

Browse by Department
Format:
Online
Author:
Dalton, Jack Robert
Dept./Program:
Mathematics
Year:
2017
Degree:
MS
Abstract:
A number of exciting recent developments in the field of sieve theory have been done concerning bounded gaps between prime numbers. One of the main techniques used in these papers is a modified version of Selberg's Sieve from the 1940's. While there are a number of sources that explain the original sieve, most, if not all, are quite inaccessible to those without significant experience in analytic number theory. The goal of this exposition is to change that. The statement and proof of the general form of Selberg's sieve is, by itself, difficult to understand and appreciate. For this reason, the inital exposition herein will be about one particular application: to recover Chebysheff's upper bound on the order of magnitude of the number of primes less than a given number. As Selberg's sieve follows some of the same initial steps as the more elementary sieve of Eratosthenes, this latter sieve will be worked through as well. To help the reader get a better sense of Selberg's sieve, a few particular applications are worked through, including an upper bound on the number of twin primes less than a number. This will then be used to show the convergence of the reciprocals of the twin primes.