Are there arbitrarily long arithmetic progressions in the sequence of twin primes? II

作者：Pintz Janos^*

来源：Proceedings of the Steklov Institute of Mathematics, 2012, 276(1): 222-227.

DOI：10.1134/S008154381201018X

In an earlier work it was shown that the Elliott-Halberstam conjecture implies the existence of infinitely many gaps of size at most 16 between consecutive primes. In the present work we show that assuming similar conditions not just for the primes but for functions involving both the primes and the Liouville function, we can assure not only the infinitude of twin primes but also the existence of arbitrarily long arithmetic progressions in the sequence of twin primes. An interesting new feature of the work is that the needed admissible distribution level for these functions is just 3/4 in contrast to the Elliott-Halberstam conjecture.

• 出版日期2012-4