25 citations · 28 across the 6 of their papers we have counts for
6 papers
Primes in Tuples I
D. A. Goldston, J. Pintz, C. Y. Yildirim
We introduce a method for showing that there exist prime numbers which are very close together. The method depends on the level of distribution of primes in arithmetic progressions…
Small gaps between primes or almost primes
D. A. Goldston, S. W. Graham, J. Pintz +1
Let denote the prime. Goldston, Pintz, and Yildirim recently proved that We give an alternative proof of…
Small Gaps between Primes Exist
D. A. Goldston, Y. Motohashi, J. Pintz +1
In the recent preprint [3], Goldston, Pintz, and Yıldırım established, among other things, $$ \liminf_{n\to\infty}{p_{n+1}-p_n\over\log p_n}=0,\leqno(0) $$ with the th pri…
Small Gaps Between Primes I
D. A. Goldston, C. Y. Yildirim
We use short divisor sums to approximate prime tuples and moments for primes in short intervals. By connecting these results to classical moment problems we are able to prove that…
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 …
Notes on Pair Correlation of Zeros and Prime Numbers
D. A. Goldston
These notes are based on my four lectures given at the Newton Institute in April 2004 during the Recent Perspectives in Random Matrix Theory and Number Theory Workshop. Their purpo…