Glasnik matematički, Vol. 50 No. 1, 2015.
Izvorni znanstveni članak
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
Sažetak
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).
Ključne riječi
Index form equations; minimal index; totally real bicyclic biquadratic fields; simultaneous Pellian equations; p-adic case
Hrčak ID:
140084
URI
Datum izdavanja:
15.6.2015.
Posjeta: 823 *