Page 1 Next

Displaying 1 – 20 of 141

Showing per page

Bases of canonical number systems in quartic algebraic number fields

Horst Brunotte, Andrea Huszti, Attila Pethő (2006)

Journal de Théorie des Nombres de Bordeaux

Canonical number systems can be viewed as natural generalizations of radix representations of ordinary integers to algebraic integers. A slightly modified version of an algorithm of B. Kovács and A. Pethő is presented here for the determination of canonical number systems in orders of algebraic number fields. Using this algorithm canonical number systems of some quartic fields are computed.

Binomial squares in pure cubic number fields

Franz Lemmermeyer (2012)

Journal de Théorie des Nombres de Bordeaux

Let K = ( ω ) , with ω 3 = m a positive integer, be a pure cubic number field. We show that the elements α K × whose squares have the form a - ω for rational numbers a form a group isomorphic to the group of rational points on the elliptic curve E m : y 2 = x 3 - m . This result will allow us to construct unramified quadratic extensions of pure cubic number fields K .

Capitulation dans certaines extensions non ramifiées de corps quartiques cycliques

Abdelmalek Azizi, Mohammed Talbi (2008)

Archivum Mathematicum

Let K = k ( - p ε l ) with k = ( l ) where l is a prime number such that l = 2 or l 5 m o d 8 , ε the fundamental unit of k , p a prime number such that p 1 m o d 4 and ( p l ) 4 = - 1 , K 2 ( 1 ) the Hilbert 2 -class field of K , K 2 ( 2 ) the Hilbert 2 -class field of K 2 ( 1 ) and G = Gal ( K 2 ( 2 ) / K ) the Galois group of K 2 ( 2 ) / K . According to E. Brown and C. J. Parry [7] and [8], C 2 , K , the Sylow 2 -subgroup of the ideal class group of K , is isomorphic to / 2 × / 2 , consequently K 2 ( 1 ) / K contains three extensions F i / K ...

Currently displaying 1 – 20 of 141

Page 1 Next