Bounded Gaps between Products of Special Primes
Name
mathematics-02-00037.pdf
Size
1.11 MB
Format
Adobe PDF
Checksum (MD5)
91838554452a08fdb12431686eda769b
Author(s)
Li, Shiyu
Chung, Ping Ngai
Date Issued
March 2014
Journal
Mathematics
Publisher
MDPI AG
Citation
Chung, Ping and Li, Shiyu. "Bounded Gaps between Products of Special Primes." Mathematics 2, 1 (March 2014): 37-52 © 2014 The Author(s)
Version
Final published version
Abstract
In their breakthrough paper in 2006, Goldston, Graham, Pintz and Yıldırım 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
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.3390/math2010037
