Norm-Euclidean Galois fields and the Generalized Riemann Hypothesis
نویسنده
چکیده
Assuming the Generalized Riemann Hypothesis (GRH), we show that the norm-Euclidean Galois cubic fields are exactly those with discriminant ∆ = 7, 9, 13, 19, 31, 37, 43, 61, 67, 103, 109, 127, 157 . 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 ` and conductor f . Assume the GRH for ζK(s). If 38(`− 1)(log f) log log f < f , then K is not norm-Euclidean.
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