ALMOST‐PRIME k‐TUPLES. Issue 1 (6th September 2013)

• Record Type: Journal Article
• Authors: Maynard, James
• Is Part Of: Mathematika. Volume 60:Issue 1(2014)
• Page Start: 108
• Page End: 138
• Publication Date: 2013-09-06
• Subjects: 11N05 -- 11N35 -- 11N36 (primary); Mathematics -- Periodicals; 510.5
• DOI: 10.1112/S0025579313000028
• Languages: English
• ISSNs: 0025-5793

Abstract

Abstract: Let k ≥ 2 and Π ( n ) = ∏ 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 .