Small Prime Gaps in Abelian Number Fields

Details Small Prime Gaps in Abelian Number Fields Small Prime Gaps in Abelian Number Fields

2011-11-29

arxiv.org/abs/1111.6692v1

Mathematics

Number Theory

18 pages

Scientific paper

We prove an analogue of a result by Goldston, Pintz and Yildirim for small gaps between primes that split completely in an abelian number field. We prove both a conditional result assuming the Elliott-Halberstam conjecture, and an unconditional result. We also give another proof of the same result in the special case of a quadratic extension of class number 1, which relies on a generalization of the Bombieri-Vinogradov theorem for quadratic number fields.

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