On elements with index of the form 2a3b in a parametric family of biquadratic fields
Borka Jadrijević · Glasnik Matematicki · 2015
In this paper we give some results about primitive integral elements α in the family of bicyclic biquadratic fields Lc = Q( (c -2) c, (c + 4) c) which have index of the form µ (α) = 2 a 3 b and coprime coordinates in given integral bases.Precisely, we show that if c ≥ 11 and α is an element with index µ (α) = 2 a 3 b ≤ c + 1, then α is an element with minimal index µ (α) = µ (Lc) = 12.We also show that for every integer C 0 ≥ 3 we can find effectively computable constants M 0 (C 0 ) and N 0 (C 0 ) such that if c ≤ C 0 , than there are no elements α with index of the form µ (α) = 2 a 3 b , where a > M (C 0 ) or b > N (C 0 ).