Small generators of number fields

Details Small generators of number fields Small generators of number fields

1996-12-17

arxiv.org/abs/math/9612229v1

Mathematics

Number Theory

Scientific paper

This is a revised version of ANT-0045.
If K is a number field of degree n with discriminant D, if K=Q(a) then
H(a)>c(n)|D|^(1/(2n-2)) where H(a) is the height of the minimal polynomial of
a. We ask if one can always find a generator a of K such that
d(n)|D|^(1/(2n-2))>H(a) holds. The answer is yes for real quadratic fields.

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