On the Stickelberger ideal and the circular units of an abelian field

1980 ◽  
Vol 62 (2) ◽  
pp. 181-234 ◽  
Author(s):  
W. Sinnott
Keyword(s):  
Abelian Field ◽  
Stickelberger Ideal ◽  
Circular Units

Stickelberger ideal and signature of circular units

1996 ◽  
Vol 223 (1) ◽  
pp. 1-11
Author(s):  
Wolfgang Schwarz ◽  
Horst-Günter Zimmer
Keyword(s):  
Stickelberger Ideal ◽  
Circular Units

scholarly journals Circular units of an abelian field ramified at three primes

2016 ◽  
Vol 163 ◽  
pp. 296-315 ◽  
Author(s):  
Radan Kučera ◽  
Azar Salami
Keyword(s):  
Abelian Field ◽  
Circular Units

scholarly journals Formulae for the relative class number of an imaginary abelian field in the form of a determinant

2001 ◽  
Vol 163 ◽  
pp. 167-191 ◽  
Author(s):  
Radan Kučera
Keyword(s):  
Class Number ◽  
Relative Class ◽  
Abelian Field ◽  
Relative Class Number ◽  
Stickelberger Ideal ◽  
Cyclotomic Units

There is in the literature a lot of determinant formulae involving the relative class number of an imaginary abelian field. Usually such a formula contains a factor which is equal to zero for many fields and so it gives no information about the class number of these fields. The aim of this paper is to show a way of obtaining most of these formulae in a unique fashion, namely by means of the Stickelberger ideal. Moreover some new and non-vanishing formulae are derived by a modification of Ramachandra’s construction of independent cyclotomic units.

Stickelberger ideal and signature of circular units

1996 ◽  
Vol 223 (1) ◽  
pp. 1-11
Author(s):  
Wolfgang Schwarz ◽  
Horst-Günter Zimmer
Keyword(s):  
Stickelberger Ideal ◽  
Circular Units
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