On a special kind of homomorphism defined on the multiplicative group of an algebraic number field

2003 ◽  
Vol 65 (1) ◽  
pp. 31-39
Author(s):  
D. Gröger
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Multiplicative Group ◽  
Special Kind ◽  
Algebraic Number Field

On a problem in algebraic number theory

1996 ◽  
Vol 119 (2) ◽  
pp. 191-200 ◽  
Author(s):  
J. Wójcik
Keyword(s):  
Number Theory ◽  
Prime Ideal ◽  
Number Field ◽  
Algebraic Number ◽  
Multiplicative Group ◽  
Algebraic Number Field ◽  
Algebraic Number Theory ◽  
Ring Of Integers

Let K be an algebraic number field. If q is a prime ideal of the ring of integers of K and α is a number of K prime to q then Mq(α) denotes the multiplicative group generated by α modulo q. In the paper [5] there is the remark: ‘We do not know whether for all a, b, c ∈ ℚ with abc ≠ 0, |a| ≠ 1,|b| ≠ 1,|c| ≠ 1 there exist infinitely many primes q with Mq (a) = Mq (b) = Mq (c).’

scholarly journals Unit theorems on algebraic tori

1988 ◽  
Vol 112 ◽  
pp. 117-124 ◽  
Author(s):  
Hyun Kwang Kim
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Multiplicative Group ◽  
Finite Extension ◽  
Algebraic Number Field ◽  
Algebraic Tori ◽  
Algebraic Torus

Let k be a p-adic field (a finite extension of Qp) or an algebraic number field (a finite extension of Q). Let T be an algebraic torus defined over k. We denote by the character module of T (i.e. = Hom (T, Gm), where Gm is the multiplicative group.

On correspondence between orders and ideals with a normal basis in cyclic subfields of Q(ξp) of a prime degree l

2010 ◽  
Vol 60 (6) ◽  
Author(s):  
Juraj Kostra
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Normal Basis ◽  
Prime Degree ◽  
One To One

AbstractLet K be a tamely ramified cyclic algebraic number field of prime degree l. In the paper one-to-one correspondence between all orders of K with a normal basis and all ideals of K with a normal basis is given.

scholarly journals The trace-form of an algebraic number field

1973 ◽  
Vol 5 (5) ◽  
pp. 379-384 ◽  
Author(s):  
Donald Maurer
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Trace Form

scholarly journals Automorphy factors for a Hilbert modular group

1988 ◽  
Vol 30 (2) ◽  
pp. 231-236
Author(s):  
Shigeaki Tsuyumine
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Rational Number ◽  
Modular Group ◽  
Algebraic Number Field ◽  
Maximal Order ◽  
Hilbert Modular Group ◽  
Hilbert Modular ◽  
Totally Real

Let K be a totally real algebraic number field of degree n > 1, and let OK be the maximal order. We denote by гk, the Hilbert modular group SL2(OK) associated with K. On the extent of the weight of an automorphy factor for гK, some restrictions are imposed, not as in the elliptic modular case. Maass [5] showed that the weight is integral for K = ℚ(√5). It was shown by Christian [1] that for any Hilbert modular group it is a rational number with the bounded denominator depending on the group.

scholarly journals On the Hecke-Landau L-Series

1960 ◽  
Vol 16 ◽  
pp. 11-20 ◽  
Author(s):  
Tikao Tatuzawa
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Integral Domain ◽  
Algebraic Number Field

Let k be an algebraic number field of degree n = r1 + 2r2 with r1 real conjugates k(l) (1 ≦ l ≦ r1) and r2 pairs of complex conjugates k(m), k(m+r2)) (r1 + 1 ≦ m ≦ r1 + r2). Let o be the integral domain consisting of all integers in k.

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