Dixon–Selberg summation over local number fields

1992 ◽  
Vol 33 (6) ◽  
pp. 2111-2114
Author(s):  
E. Thiran ◽  
J. Weyers
Keyword(s):  
Number Fields ◽  
Local Number

scholarly journals Distribution of units of real quadratic number fields

2000 ◽  
Vol 158 ◽  
pp. 167-184 ◽  
Author(s):  
Yen-Mei J. Chen ◽  
Yoshiyuki Kitaoka ◽  
Jing Yu
Keyword(s):  
Prime Ideal ◽  
Quadratic Field ◽  
Number Fields ◽  
Prime Ideals ◽  
Positive Density ◽  
Real Quadratic Field ◽  
Quadratic Number ◽  
Ring Of Integers ◽  
Group Of Units ◽  
Real Quadratic

AbstractLet k be a real quadratic field and k, E the ring of integers and the group of units in k. Denoting by E() the subgroup represented by E of (k/)× for a prime ideal , we show that prime ideals for which the order of E() is theoretically maximal have a positive density under the Generalized Riemann Hypothesis.

Biquadratic Extensions with One Break

2002 ◽  
Vol 45 (2) ◽  
pp. 168-179 ◽  
Author(s):  
Nigel P. Byott ◽  
G. Griffith Elder
Keyword(s):  
Number Fields ◽  
Module Structure ◽  
Galois Module ◽  
Galois Module Structure ◽  
Local Number

AbstractWe explicitly describe, in terms of indecomposable ℤ2[G]-modules, the Galois module structure of ideals in totally ramified biquadratic extensions of local number fields with only one break in their ramification filtration. This paper completeswork begun in [Elder: Canad. J.Math. (5) 50(1998), 1007–1047].

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