On elements with index divisible by fixed primes in a parametric family of bicyclic biquadratic fields (CROSBI ID 615878)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
Podaci o odgovornosti
Jadrijević, Borka
engleski
On elements with index divisible by fixed primes in a parametric family of bicyclic biquadratic fields
In this talk we will present some results about primitive integral elements α in the family of bicyclic biquadratic fields L_{; ; c}; ; =Q(√((c-2)c), √((c+4)c)) which have index μ(α) divisible by fixed primes 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(L_{; ; c}; ; )=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, then there are no elements α with index of the form μ(α)=2^{; ; a}; ; 3^{; ; b}; ; , where a>M(C₀) or b>N(C₀).
index form equations; minimal index; totally real bicyclic biquadratic fields; simultaneous Pellian equations
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nije evidentirano
nije evidentirano
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Podaci o prilogu
2014.
objavljeno
Podaci o matičnoj publikaciji
ALANT 3 — Joint Conferences on Algebra, Logic and Number Theory
Bedlewo:
Podaci o skupu
ALANT 3 — Joint Conferences on Algebra, Logic and Number Theory
predavanje
08.06.2014-13.06.2014
Będlewo, Poljska