Are there arbitrarily long arithmetic progressions in the sequence of twin primes? II
Are there arbitrarily long arithmetic progressions in the sequence of twin primes? II
复制标题
孪生素数序列中是否存在任意长的算术级数？
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
J. Pintz
中科院分区：
文献类型：
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作者：
J. Pintz
在早期的工作中，艾略特-哈尔伯斯坦猜想表明，连续素数之间存在无限多个大小最多为 16 的间隙。在目前的工作中，我们表明，不仅对素数而且对涉及素数和刘维尔函数的函数都假设类似的条件，我们不仅可以保证孪生素数的无限性，而且可以保证孪生素数序列中任意长算术级数的存在。这项工作的一个有趣的新特点是，与 Elliott-Halberstam 猜想相比，这些函数所需的允许分布水平仅为 3/4。
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.