Patterns of Primes in Arithmetic Progressions
Patterns of Primes in Arithmetic Progressions
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算术级数中素数的模式
DOI：
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发表时间：
2015
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通讯作者：
J. Pintz
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文献类型：
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作者：
J. Pintz
在张文中证明了连续素数之间存在无穷多个有界间隔之后，作者证明了存在有界d使得存在任意长的素数算术级数，且对于级数的每个元素，p ′ = p + d是p之后的素数。这是对Zhang和Green-Tao的结果的普遍推广。在目前的工作中，它表明，对于每一个m，我们有一个有界的m元组的素数，使这种配置（即整数翻译这个m元组）出现在任意长的算术级数的序列中的所有素数。事实上，我们表明，这是真实的一个积极的比例，所有的m元组。这是格林-陶和梅纳德/陶著名作品的共同概括。
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive primes the author showed the existence of a bounded d such that there are arbitrarily long arithmetic progressions of primes with the property that p ′ = p + d is the prime following p for each element of the progression. This was a common generalization of the results of Zhang and Green-Tao. In the present work it is shown that for every m we have a bounded m-tuple of primes such that this configuration (i.e. the integer translates of this m-tuple) appear as arbitrarily long arithmetic progressions in the sequence of all primes. In fact we show that this is true for a positive proportion of all m-tuples. This is a common generalization of the celebrated works of Green-Tao and Maynard/Tao.