BEST POSSIBLE DENSITIES OF DICKSON m-TUPLES, AS A CONSEQUENCE OF ZHANG-MAYNARD-TAO
نویسندگان
چکیده
We determine for what proportion of integers h one now knows that there are infinitely many prime pairs p, p+ h as a consequence of the Zhang-Maynard-Tao theorem. We consider the natural generalization of this to k-tuples of integers, and we determine the limit of what can be deduced assuming only the Zhang-Maynard-Tao theorem.
منابع مشابه
Bounded Gaps between Primes in Number Fields and Function Fields
The Hardy–Littlewood prime k-tuples conjecture has long been thought to be completely unapproachable with current methods. While this sadly remains true, startling breakthroughs of Zhang, Maynard, and Tao have nevertheless made significant progress toward this problem. In this work, we extend the Maynard-Tao method to both number fields and the function field Fq(t).
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