Primes in short arithmetic progressions
2015 ◽
Vol 11
(05)
◽
pp. 1499-1521
◽
Keyword(s):
Let x, h and Q be three parameters. We show that, for most moduli q ≤ Q and for most positive real numbers y ≤ x, every reduced arithmetic progression a( mod q) has approximately the expected number of primes p from the interval (y, y + h], provided that h > x1/6+ϵ and Q satisfies appropriate bounds in terms of h and x. Moreover, we prove that, for most moduli q ≤ Q and for most positive real numbers y ≤ x, there is at least one prime p ∈ (y, y + h] lying in every reduced arithmetic progression a( mod q), provided that 1 ≤ Q2 ≤ h/x1/15+ϵ.
2012 ◽
Vol DMTCS Proceedings vol. AQ,...
(Proceedings)
◽
Keyword(s):
2018 ◽
Vol 7
(1)
◽
pp. 77-83
Keyword(s):
Keyword(s):
2009 ◽
Vol 2009
◽
pp. 1-11
◽
Keyword(s):
2009 ◽
Vol 05
(04)
◽
pp. 625-634
2014 ◽
Vol 33
(2)
◽
pp. 59-67
Keyword(s):