The Goldston-Pintz-Yildirim Sieve and Maximal Gaps

Details The Goldston-Pintz-Yildirim Sieve and Maximal Gaps The Goldston-Pintz-Yildirim Sieve and Maximal Gaps

2008-11-20

arxiv.org/abs/0811.3256v2

Mathematics

Number Theory

Updated to correct typographical errors and the error term in Theorem 2

Scientific paper

One field of particular interest in Number Theory concerns the gaps between consecutive primes. Within the last few years, very important results have been achieved on how small these gaps can be. The strongest of these results were obtained by Dan Goldston, Janos Pintz and Cem Yalcin Yildirim. The present work begins by generalizing their results so that they can be applied to related problems in a more direct manner. Additionally, we improve the bound for $F_2$ (concerning the maximal gap in a block of three primes) obtained by the authors' first paper with our generalization.

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