Small gaps between products of two primes

Goldston, D. A.; Graham, S. W.; Pintz, János; Yıldırım, Cem Yalçın

doi:10.1112/plms/pdn046

Cited by 40 publications

(70 citation statements)

References 27 publications

(42 reference statements)

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“…There are 42 such monomials, and with k = 105 we can calculate the 42 × 42 rational symmetric matrices M 1 and M 2 corresponding to the coefficients of the quadratic forms I k (F) and k m=1 J k (F). We then find 3 3 An ancillary Mathematica R file detailing these computations is available alongside this paper at www.arxiv.org.…”

Section: Choice Of Weight For Small Kmentioning

confidence: 99%

Small gaps between primes

Maynard¹

2015

Ann. Math.

243

390

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Abstract. We introduce a refinement of the GPY sieve method for studying prime k-tuples and small gaps between primes. This refinement avoids previous limitations of the method, and allows us to show that for each k, the prime k-tuples conjecture holds for a positive proportion of admissible k-tuples. In particular, lim inf n (p n+m − p n ) < ∞ for any integer m. We also show that lim inf(p n+1 − p n ) ≤ 600, and, if we assume the Elliott-Halberstam conjecture, that lim inf n (p n+1 − p n ) ≤ 12 and lim inf n (p n+2 − p n ) ≤ 600.

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Section: Choice Of Weight For Small Kmentioning

confidence: 99%

Small gaps between primes

Maynard¹

2015

Ann. Math.

243

390

View full text Add to dashboard Cite

show abstract

“…, log |r k | log R and set y r 1 ,...,r k = 0 otherwise. In order to evaluate the summations of y r 1 ,...,r k , we will need the following lemma, which is an analogue of a result of Goldston, Graham, Pintz, and Yıldırım [3,Lemma 4]. (This result also appears as Lemma 6.1 in [11].)…”

Section: (24)mentioning

confidence: 99%