scholarly journals Refined Lower Bounds on the 2-Class Number of the Hilbert 2-Class Field of Imaginary Quadratic Number Fields with Elementary 2-Class Group of Rank 3

1999 ◽  
Vol 76 (2) ◽  
pp. 167-177 ◽  
Author(s):  
Elliot Benjamin ◽  
Charles J. Parry
Keyword(s):  
Lower Bounds ◽  
Class Number ◽  
Class Group ◽  
Number Fields ◽  
Quadratic Number ◽  
Class Field ◽  
Quadratic Number Fields ◽  
Imaginary Quadratic Number

scholarly journals Using Continued Fractions to Compute Iwasawa Lambda Invariants of Imaginary Quadratic Number Fields

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Jordan Schettler
Keyword(s):  
Continued Fractions ◽  
Class Number ◽  
Continued Fraction ◽  
Number Fields ◽  
Quadratic Number ◽  
Continued Fraction Expansion ◽  
Quadratic Number Fields ◽  
Analogous Formula ◽  
Partial Quotients ◽  
Imaginary Quadratic Number

Let l>3 be a prime such that l≡3 (mod 4) and Q(l) has class number 1. Then Hirzebruch and Zagier noticed that the class number of Q(-l) can be expressed as h(-l)=(1/3)(b1+b2+⋯+bm)-m where the bi are partial quotients in the “minus” continued fraction expansion l=[[b0;b1,b2,…,bm¯]]. For an odd prime p≠l, we prove an analogous formula using these bi which computes the sum of Iwasawa lambda invariants λp(-l)+λp(-4) of Q(-l) and Q(-1). In the case that p is inert in Q(-l), the formula pleasantly simplifies under some additional technical assumptions.

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