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Results tagged with sieve-theory
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user 37555
2
votes
A sieve with two parameters
Such a sieve could only exist under rather special conditions. The easiest case would be $\Omega_p=\{0\}$, $z=\sqrt{x}$. In this case the sifted set consists of all integers of the form $pn\leq x$, wh …
4
votes
Shifted primes avoiding a set of divisors
No, $\delta_y$ need not tend to 0. Take a rapidly increasing sequence of integers $y_n$. Then define the set $B$ as $\{p-1|\exists n: y_n\leq p\leq 2y_n\}$. Then we have
\begin{eqnarray*}
\delta_{y_n} …
12
votes
0
answers
626
views
Sieve bound for prime $k$-tuples
Let $d_1<d_2<\dots<d_k$ be integers. Then the number of integers $n\leq x$, such that $n+d_1, n+d_2, \ldots, n+d_k$ are simultaneously prime, is bounded above by
$$
\mathfrak{S}(d_1, \ldots, d_k) (Ck) …