Naslov
On elements with index divisible by fixed primes in a parametric family of bicyclic biquadratic fields

Autori
Jadrijević, Borka

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
ALANT 3 — Joint Conferences on Algebra, Logic and Number Theory / - Bedlewo, 2014

Skup
ALANT 3 — Joint Conferences on Algebra, Logic and Number Theory

Mjesto i datum
Będlewo, Poljska, 08.06.2014. - 13.06.2014

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
index form equations; minimal index; totally real bicyclic biquadratic fields; simultaneous Pellian equations

Sažetak
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).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA