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The Selberg Sieve and prime pairs Duarte, Martin Christopher
Abstract
This paper gives an exposition of the Selberg Sieve and its application to the sifting of prime pairs. In particular, Selberg's methods are applied to the sifting approach of Eratosthenes and to an alternate sifting approach presented by the author. The results obtained are then used to show that the sum of the reciprocals of the twin primes (and similarly for general prime pairs) is convergent or finite. This paper is intended to be mostly self-contained and will hopefully be readable to someone with little background in the area of Sieve Theory.
Item Metadata
| Title |
The Selberg Sieve and prime pairs
|
| Creator | |
| Publisher |
University of British Columbia
|
| Date Issued |
2005
|
| Description |
This paper gives an exposition of the Selberg Sieve and its application to the
sifting of prime pairs. In particular, Selberg's methods are applied to the sifting
approach of Eratosthenes and to an alternate sifting approach presented
by the author. The results obtained are then used to show that the sum of
the reciprocals of the twin primes (and similarly for general prime pairs) is
convergent or finite. This paper is intended to be mostly self-contained and
will hopefully be readable to someone with little background in the area of
Sieve Theory.
|
| Genre | |
| Type | |
| Language |
eng
|
| Date Available |
2009-12-11
|
| Provider |
Vancouver : University of British Columbia Library
|
| Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
|
| DOI |
10.14288/1.0080068
|
| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
|
| Graduation Date |
2005-05
|
| Campus | |
| Scholarly Level |
Graduate
|
| Aggregated Source Repository |
DSpace
|
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.