A generalization of the Goldston-Pintz-Yildirim prime gaps result to number fields

作者：Kaptan D A^*

来源：Acta Mathematica Hungarica, 2013, 141(1-2): 84-112.

DOI：10.1007/s10474-013-0296-x

• distribution of primes
• algebraic number field

D. A. Goldston, J. Pintz and C. Y. Yildirim [3] proved the existence of infinitely many prime pairs whose difference is arbitrarily small compared to the average gap, namely
lim inf(n ->infinity) p(n+1) -p(n)/log p(n) = 0.
In the present work we generalize their result to totally real number fields. We prove that if omega (0) and omega (1) run over distinct prime elements of the number field, then
lim inf (omega 0,omega 1) vertical bar N(omega 1-omega 0)/N-omega 0 vertical bar = 0.

• 出版日期2013-10