Divisibility of Class Numbers of Quadratic Fields: Qualitative Aspects

2018 ◽  
pp. 247-264 ◽  
Author(s):  
Kalyan Chakraborty ◽  
Azizul Hoque ◽  
Richa Sharma
Keyword(s):  
Quadratic Fields ◽  
Class Numbers

scholarly journals On the Insolubility of a Class of Diophantine Equations and the Nontriviality of the Class Numbers of Related Real Quadratic Fields of Richaud-Degert Type

1987 ◽  
Vol 105 ◽  
pp. 39-47 ◽  
Author(s):  
R. A. Mollin
Keyword(s):  
Diophantine Equations ◽  
Quadratic Fields ◽  
Class Numbers ◽  
Real Quadratic Fields ◽  
Integer Solutions ◽  
The Relationship ◽  
Real Quadratic

Many authors have studied the relationship between nontrivial class numbers h(n) of real quadratic fields and the lack of integer solutions for certain diophantine equations. Most such results have pertained to positive square-free integers of the form n = l2 + r with integer >0, integer r dividing 4l and — l<r<l. For n of this form, is said to be of Richaud-Degert (R-D) type (see [3] and [8]; as well as [2], [6], [7], [12] and [13] for extensions and generalizations of R-D types.)

scholarly journals Class numbers of imaginary quadratic fields

2003 ◽  
Vol 73 (246) ◽  
pp. 907-939 ◽  
Author(s):  
Mark Watkins
Keyword(s):  
Quadratic Fields ◽  
Class Numbers ◽  
Imaginary Quadratic Fields
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