Small gaps between the set of products of at most two primes
Keiju Sono
TL;DR
This paper extends the application of Maynard and Tao's method to analyze the distribution of products of two primes, improving results on small gaps between such numbers and primes.
Contribution
It introduces new bounds on small gaps between E2-numbers and primes by adapting advanced sieve techniques.
Findings
Improved bounds on small gaps between E2-numbers and primes.
Enhanced understanding of the distribution of products of two primes.
Application of Maynard and Tao's method to E2-numbers.
Abstract
In this paper, we apply the method of Maynard and Tao to the set of products of two distinct primes (E2-numbers). We obtain several results on the distribution of E2-numbers and primes. Among others, the result of Goldston, Pintz, Yildirim and Graham on small gaps between m consecutive E2-numbers is improved.
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Taxonomy
TopicsAnalytic Number Theory Research · Limits and Structures in Graph Theory · Algebraic Geometry and Number Theory