Norm-Euclidean Galois fields and the Generalized Riemann Hypothesis

Details Norm-Euclidean Galois fields and the Generalized Riemann Hypothesis Norm-Euclidean Galois fields and the Generalized Riemann Hypothesis

2011-02-10

arxiv.org/abs/1102.2043v2

Mathematics

Number Theory

Scientific paper

Assuming the Generalized Riemann Hypothesis (GRH), we show that the norm-Euclidean Galois cubic fields are exactly those with discriminant $\Delta=7^2,9^2,13^2,19^2,31^2,37^2,43^2,61^2,67^2,103^2,109^2,127^2,157^2$. A large part of the proof is in establishing the following more general result: Let $K$ be a Galois number field of odd prime degree $\ell$ and conductor $f$. Assume the GRH for $\zeta_K(s)$. If $38(\ell-1)^2(\log f)^6\log\log f

Affiliated with

Also associated with

No associations

Rating

Norm-Euclidean Galois fields and the Generalized Riemann Hypothesis does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Norm-Euclidean Galois fields and the Generalized Riemann Hypothesis, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Norm-Euclidean Galois fields and the Generalized Riemann Hypothesis will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-694205