scholarly journals Simultaneous Asymptotic Diophantine Approximations to a Basis of a Real Number Field

1971 ◽  
Vol 42 ◽  
pp. 79-87 ◽  
Author(s):  
William W. Adams
Keyword(s):  
Real Number ◽  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Diophantine Approximations ◽  
Real Number Field

The purpose of this paper is to prove the following result.Theorem 1. Let K be a real algebraic number field of degree m = n + 1. Let 1, β1, …, βn be a basis of K.

scholarly journals On a conjecture of Littlewood in Diophantine approximations

1985 ◽  
Vol 32 (3) ◽  
pp. 379-387 ◽  
Author(s):  
S. Krass
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Diophantine Approximations

A conjecture of Littlewood States that for arbitrary , and any ε > 0 there exist m0 ≠ 0, m1,…,mn so that . In this paper we show this conjecture holds for all ξ̲ = (ξ1,…,ξn) such that 1, ξ1,…,ξn is a rational bass of a real algebraic number field of degree n+1.

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 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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