Bounded gaps between Gaussian primes
نویسندگان
چکیده
منابع مشابه
Bounded gaps between primes
It is proved that lim inf n→∞ (pn+1 − pn) < 7× 10, where pn is the n-th prime. Our method is a refinement of the recent work of Goldston, Pintz and Yildirim on the small gaps between consecutive primes. A major ingredient of the proof is a stronger version of the Bombieri-Vinogradov theorem that is applicable when the moduli are free from large prime divisors only (see Theorem 2 below), but it ...
متن کاملBounded gaps between primes in Chebotarev sets
© 2014 Thorner; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/), which permits distribution, public display, and publicly performance, making multiple copies, distribution of derivative works, provided the original work is properly cited. This license requir...
متن کاملBounded gaps between products of distinct primes
*Correspondence: [email protected] 2Department of Mathematics, Princeton University, Princeton, NJ 08544, USA Full list of author information is available at the end of the article Abstract Let r ≥ 2 be an integer. We adapt the Maynard–Tao sieve to produce the asymptotically best-known bounded gaps between products of r distinct primes. Our result applies to positive-density subsets of the pr...
متن کاملBounded gaps between products of special primes
In their breakthrough paper in 2006, Goldston, Graham, Pintz, and Yıldırım 1 proved several results about bounded gaps between products of two distinct primes. Frank 2 Thorne expanded on this result, proving bounded gaps in the set of square-free numbers with 3 r prime factors for any r ≥ 2, all of which are in a given set of primes. His results yield 4 applications to divisibility of class num...
متن کاملBounded 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).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2017
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2016.07.008