A note on generators of number fields

Details A note on generators of number fields A note on generators of number fields

2012-03-22

arxiv.org/abs/1203.4976v1

Mathematics

Number Theory

Scientific paper

We establish upper bounds for the smallest height of a generator of a number field $k$ over the rational field $\Q$. Our first bound applies to all number fields $k$ having at least one real embedding. We also give a second conditional result for all number fields $k$ such that the Dedekind zeta-function associated to the Galois closure of $k/\Q$ satisfies GRH. This provides a partial answer to a question of W. Ruppert.

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