Small generators of number fields, by Wolfgang M. Ruppert
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
The answer is yes for real quadratic fields.
(This is a revised version.)
Wolfgang M. Ruppert <email@example.com>