Hermitian Modules in Galois Extensions of Number Fields and Adams Operations

1992 ◽  
Vol 135 (2) ◽  
pp. 271 ◽  
Author(s):  
B. Erez ◽  
M. J. Taylor
Keyword(s):  
Number Fields ◽  
Galois Extensions ◽  
Adams Operations

scholarly journals Solitary Galois Extensions of Algebraic Number Fields

1995 ◽  
Vol 50 (1) ◽  
pp. 1-32 ◽  
Author(s):  
R.M. Guralnick ◽  
L. Stern
Keyword(s):  
Algebraic Number ◽  
Number Fields ◽  
Algebraic Number Fields ◽  
Galois Extensions

ON THE DISTRIBUTION OF CYCLIC NUMBER FIELDS OF PRIME DEGREE

2012 ◽  
Vol 08 (06) ◽  
pp. 1463-1475
Author(s):  
SEOK HYEONG LEE ◽  
GYUJIN OH
Keyword(s):  
Riemann Hypothesis ◽  
Error Term ◽  
London Math ◽  
Number Fields ◽  
Positive Real ◽  
Galois Extensions ◽  
Prime Degree ◽  
Abelian Extensions ◽  
Generalized Riemann Hypothesis

Let NCp(X) denote the number of Cp Galois extensions of ℚ with absolute discriminant ≤ X. A well-known theorem of Wright [Density of discriminants of abelian extensions, Proc. London Math. Soc. 58 (1989) 17–50] implies that when p is prime, we have [Formula: see text] for some positive real c(p). In this paper, we improve this result by reducing the secondary error term to [Formula: see text]. Moreover, under Generalized Riemann Hypothesis, we obtain the following stronger result [Formula: see text] Here Rp(x) ∈ ℝ[x] is a polynomial of degree ⌊p(p-2)/3⌋-1. This confirms a speculation of Cohen, Diaz y Diaz and Olivier [Counting discriminants of number fields, J. Théor. Nombres Bordeaux 18 (2006) 573–593] in the case of C3 extensions.

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