Bounded Gaps between Products of Special Primes

Ping Ngai Chung and Shiyu Li
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Ping Ngai Chung: Massachusetts Institute of Technology, 305 Memorial Drive, Cambridge, MA 02139, USA
Shiyu Li: University of California, Berkeley, 1676 S. Blaney Ave. San Jose, CA 95129, USA

Mathematics, 2014, vol. 2, issue 1, 1-16

Abstract: In their breakthrough paper in 2006, Goldston, Graham, Pintz and Y?ld?r?m proved several results about bounded gaps between products of two distinct primes. Frank Thorne expanded on this result, proving bounded gaps in the set of square-free numbers with r prime factors for any r ? 2, all of which are in a given set of primes. His results yield applications to the divisibility of class numbers and the triviality of ranks of elliptic curves. In this paper, we relax the condition on the number of prime factors and prove an analogous result using a modified approach. We then revisit Thorne’s applications and give a better bound in each case.

Keywords: bounded prime gaps; square-free numbers; modular elliptic curves (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2014
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