Small Prime Gaps in Abelian Number Fields

2011/11/29 by Alexandra Musat, Musat, Alexandra Mihaela
Mathematics · #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.1111.6692

Abstract

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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