2014/10/31 by Carl Pomerance, Andrew Granville, Daniel M. Kane +3 · 1 citation
Computer Science · Mathematics · #Algebra over a field #Analytic Number Theory Research #Analytic number theory #Art history #Combinatorics #Computability, Logic, AI Algorithms #Computer science #Discrete mathematics #Euler's formula #Euler's totient function #Generalization #History #History and Theory of Mathematics #Honor #Humanities #Law #Limit (mathematics) #Mathematical analysis #Mathematics #Multiplicative number theory #Natural number #Number theory #Philosophy #Prime (order theory) #Prime factor #Prime number #Prime number theorem #Pure mathematics #Riemann hypothesis #Theology #Tuple #Zhàng #math.CO #math.NT
paper · pdf · doi:10.1007/978-3-319-22240-0
9 pages. Final version. Some minor changes, Analytic Number Theory - In Honor of Helmut Maier's 60th Birthday, Springer, 2015
openalex publication_date 2015/01/01 · arxiv created 2015/10/20 · arxiv updated 2017/06/12 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28
We determine for what proportion of integers h one now knows that there are infinitely many prime pairs p, p+h as a consequence of the Zhang-Maynard-Tao theorem. We consider the natural generalization of this to k-tuples of integers, and we determine the limit of what can be deduced assuming only the Zhang-Maynard-Tao theorem.