Bounded gaps between products of distinct primes

Yang Liu, Peter S. Park, Zhuo Qun Song

Type: Article

Publication Date: 2017-07-24

Citations: 1

DOI: https://doi.org/10.1007/s40993-017-0089-3

Abstract

Let $$r \ge 2$$ be an integer. We adapt the Maynard–Tao sieve to produce the asymptotically best-known bounded gaps between products of r distinct primes. Our result applies to positive-density subsets of the primes that satisfy certain equidistribution conditions. This improves on the work of Thorne and Sono.

Locations

Research in Number Theory - View - PDF

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+	ON THE REPRESENTATION OF A LARGER EVEN INTEGER AS THE SUM OF A PRIME AND THE PRODUCT OF AT MOST TWO PRIMES	1973	Chen Jing-Run
+ PDF Chat	The 𝑘^{𝑡ℎ} prime is greater than 𝑘(ln𝑘+lnln𝑘-1) for 𝑘≥2	1999	Pierre Dusart
+ PDF Chat	Small gaps between primes or almost primes	2009	D. A. Goldston S. W. Graham J. Pintz C. Y. Yıldırım
+ PDF Chat	Bounded Gaps between Products of Special Primes	2014	Ping Ngai Chung Shiyu Li
+ PDF Chat	Primes in arithmetic progressions to large moduli	1986	Enrico Bombieri John Friedlander Henryk Iwaniec
+ PDF Chat	Primes in tuples II	2010	D. A. Goldston J. Pintz C. Y. Yıldırım
+	Divisibility of Class Numbers of Imaginary Quadratic Fields	2000	K. Soundararajan
+ PDF Chat	Small gaps between primes	2014	James Maynard
+ PDF Chat	None	1997	Ken Ono
+ PDF Chat	Small gaps between products of two primes	2008	D. A. Goldston S. W. Graham J. Pintz C. Y. Yıldırım