59 citations · 72 across the 7 of their papers we have counts for
7 papers
Small gaps between almost primes, the parity problem, and some conjectures of Erdős on consecutive integers II
Daniel A. Goldston, Sidney W. Graham, Apoorva Panidapu +3
This paper is intended as a sequel to a paper arXiv:0803.2636 written by four of the coauthors here. In the paper, they proved a stronger form of the Erdős-Mirksy conjecture which…
Primes in Tuples IV: Density of small gaps between consecutive primes
D. A. Goldston, J. Pintz, C. Y. Yildirim
We show that a positive proportion of all gaps between consecutive primes are small gaps. We provide several quantitative results, some unconditional and some conditional, in this…
Positive Proportion of Small Gaps Between Consecutive Primes
D. A. Goldston, J. Pintz, C. Y. Yildirim
We prove that a positive proportion of the gaps between consecutive primes are short gaps of length less than any fixed fraction of the average spacing between primes.
Small gaps between almost primes, the parity problem, and some conjectures of Erdos on consecutive integers
D. A. Goldston, S. W. Graham, J. Pintz +1
In a previous paper, the authors proved that in any system of three linear forms satisfying obvious necessary local conditions, there are at least two forms that infinitely often a…
Small gaps between products of two primes
D. A. Goldston, S. W. Graham, J. Pintz +1
Let denote the number that is a product of exactly two distinct primes. We prove that This sharpens an earlier result…
Higher Correlations of Divisor Sums Related to Primes II: Variations of the error term in the prime number theorem
D. A. Goldston, C. Y. Yildirim
We calculate the triple correlations for the truncated divisor sum . The 's behave over certain averages just as the prime counting von Mangoldt function …