25 citations · 40 across the 9 of their papers we have counts for
6 papers · 2 filters
The Path to Recent Progress on Small Gaps Between Primes
D. A. Goldston, J. Pintz, C. Y. Yildirim
This paper describes some of the ideas used in the development of our work on small gaps between primes.
A note on S(T) and the zeros of the Riemann zeta-function
D. A. Goldston, S. M. Gonek
Let denote the argument of the Riemann zeta-function at the point . Assuming the Riemann Hypothesis, we sharpen the constant in the best currently known bounds…
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…