کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6415312 1630643 2017 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Bounded gaps between Gaussian primes
ترجمه فارسی عنوان
شکاف های محدود بین نخستین گاوسی
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

We show that there are infinitely many distinct rational primes of the form p1=a2+b2 and p2=a2+(b+h)2, with a,b,h integers, such that |h|≤246. We do this by viewing a Gaussian prime c+di as a lattice point (c,d) in R2 and showing that there are infinitely many pairs of distinct Gaussian primes (c1,d1) and (c2,d2) such that the Euclidean distance between them is bounded by 246. Our method, motivated by the work of Maynard [9] and the Polymath project [13], is applicable to the wider setting of imaginary quadratic fields with class number 1 and yields better results than those previously obtained for gaps between primes in the corresponding number rings.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 171, February 2017, Pages 449-473
نویسندگان
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