ALMOST-PRIME k-TUPLES. Issue 1 (6th September 2013) - Maynard, James
Abstract: Let k≥ 2 and Π (n)= olimits_i= 1^k (a_i n+ b_i ) for some integers a_i, b_i ( 1≤ i≤ k ). Suppose that Π (n) has no fixed prime divisors. Weighted sieves have shown for infinitely many integers n that the number of prime factors Ω (Π (n)) of Π (n) is at most r_k , for some integer r_k depending only on k . We use a new kind of weighted sieve to improve the possible values of r_k when k≥ 4 .