Bounded gaps between primes

By Yitang Zhang. 2014

613 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2e748464dedf02677a7c7a78b830f7cedcb1472c

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Variants of the Selberg sieve, and bounded intervals containing many primes (2014, methodology): “The first unconditional bound on H1 was established in a breakthrough work of Zhang [65]: Theorem 1.”
Small gaps between primes (2013, methodology): “…Yıldırım introduced a new method for counting tuples of primes, and this allowed them to show that (1.1) lim inf The recent breakthrough of Zhang [9] managed to extend this work to prove (1.2) lim inf n ( p n +1 − p n ) ≤ 70 000 000 , thereby establishing for the ﬁrst time the existence of…”
Logical Induction (2016, background): “Indeed, when Zhang (2014) proved a bound on the gap between primes, we were tempted to increase our credence in the twin prime conjecture.”
Dense clusters of primes in subsets (2014, background): “Zhang [20] succeeded in proving such an extension 3 , and as a consequence showed the existence of bounded gaps between primes.”
Sums of Kloosterman sums in arithmetic progressions, and the error term in the dispersion method (2015, neutral): “It has received a large publicity recently with the breakthrough of Zhang [57] (see also [47]), giving the first proof of the existence of infinitely many bounded gaps between primes (which was shown later by Maynard [43] and Tao (unpublished) not to require such strong results).”
On the exponent of distribution of the ternary divisor function (2013, background): “After the first version of this paper had been submitted for publication, the arithmetic importance of the exponent of distribution of the ternary divisor function for suitable large moduli was highlighted again in Zhang’s groundbreaking work [16] on bounded gap between primes.”