Original scientific paper

https://doi.org/10.3336/gm.50.1.05

On elements with index of the form 2a3b in a parametric family of biquadratic fields

Borka Jadrijević orcid.org/0000-0002-5913-3719 ; Department of Mathematics, Faculty of Science, University of Split, Teslina 12, 21000 Split, Croatia

Abstract

In this paper we give some results about primitive integral elements α in the family of bicyclic biquadratic fields Lc= Q ( ((c-2) c)1/2, ((c+4) c)1/2) which have index of the form μ( α) =2a3b and coprime coordinates in given integral bases. Precisely, we show that if c≥11 and α is an element with index μ( α) =2a3b≤ c+1, then α is an element with minimal index μ( α) =μ( Lc) =12. We also show that for every integer C0≥3 we can find effectively computable constants M0( C0) and N0( C0) such that if c≤ C0, than there are no elements α with index of the form μ( α) =2a3b, where a>M( C0) or b>N( C0).

Keywords

Index form equations; minimal index; totally real bicyclic biquadratic fields; simultaneous Pellian equations; p-adic case

Hrčak ID:

140084

URI

https://hrcak.srce.hr/140084

Publication date:

15.6.2015.

Visits: 1.045 *