Sieve theory deals with number theoretic sieves, and sifted sets. E.g. the Sieve of Eratosthenes, Brun sieve, and other modern sieves.
Questions tagged [sieve-theory]
289 questions
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Question on Brun's Work
In Brun's Pure Sieve (using standard sieve theory notation), Brun showed that
$$S(A,P,z)=A-\sum_{p\leq z}A_p+\sum_{p_1
user81654
- 91
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1 answer
Selberg Sieve Question
The following question uses standard sieve theory terminology.
Let $A=\vert\{a_n: a_n=n(n-2); n\in[N/2,N]\}\vert$ and let $A_d=\vert\{a_n: d\vert a_n\}\vert$. If we are looking for $S^T$ the number of $a_n$ in $A$ such that $a_n$ has no prime…
user81654
- 91
2
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1 answer
Connection between Brun's Sieve and the Sieve of Eratosthenes
I have read in a couple of places that the above mentioned sieves are connected in some way. In particular, Brun's Sieve builds upon that of Eratosthenes. I do not see why this is the case and hope someone could explain the connection
user316567
- 121
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On the error term of Legendre sieve
the Legendre sieve method gives us an upper bound $S$ for the numbers that are not relatively prime to $P_{z}$ up to $x$ where $P_{z}$ is the product of prime number less than z
$S=x\prod_{p
Abdo
- 167