Imaginary quadratic fields with class group exponent 5

2008 ◽  
Vol 20 (2) ◽  
Author(s):  
D. R Heath-Brown
Keyword(s):  
Class Group ◽  
Quadratic Fields ◽  
Imaginary Quadratic Fields

scholarly journals Truncated Euler Systems over Imaginary Quadratic Fields

2009 ◽  
Vol 195 ◽  
pp. 97-111
Author(s):  
Soogil Seo
Keyword(s):  
Class Group ◽  
Quadratic Field ◽  
Abelian Extension ◽  
Iwasawa Theory ◽  
Quadratic Fields ◽  
Galois Module ◽  
Imaginary Quadratic Fields ◽  
Euler Systems ◽  
Graded Module ◽  
Elliptic Units

AbstractLet K be an imaginary quadratic field and let F be an abelian extension of K. It is known that the order of the class group ClF of F is equal to the order of the quotient UF/ElF of the group of global units UF by the group of elliptic units ElF of F. We introduce a filtration on UF/ElF made from the so-called truncated Euler systems and conjecture that the associated graded module is isomorphic, as a Galois module, to the class group. We provide evidence for the conjecture using Iwasawa theory.

Exponent of class group of certain imaginary quadratic fields

2020 ◽  
Vol 70 (4) ◽  
pp. 1167-1178
Author(s):  
Kalyan Chakraborty ◽  
Azizul Hoque
Keyword(s):  
Class Group ◽  
Quadratic Fields ◽  
Imaginary Quadratic Fields

The Parity Distribution of Traces in Imaginary Quadratic Fields

1991 ◽  
Vol 34 (2) ◽  
pp. 196-201
Author(s):  
D. S. Dummit
Keyword(s):  
Class Group ◽  
Primary Component ◽  
Quadratic Fields ◽  
Prime Ideals ◽  
Imaginary Quadratic Fields ◽  
Parity Distribution

AbstractComputations of the Iwasawa λ -invariant for imaginary quadratic fields showed a discrepancy in the proportion of even and odd traces of certain integers from these imaginary quadratic fields. This paper shows that such a discrepancy is in some sense to be expected and that the proportion of even and odd traces of principal generators of powers of prime ideals in imaginary quadratic fields is related to the 3-primary component of the class group.

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