scholarly journals The relative class number of certain imaginary abelian number fields of odd conductors

1996 ◽  
Vol 72 (3) ◽  
pp. 64-68
Author(s):  
Akira Endô
Keyword(s):  
Class Number ◽  
Number Fields ◽  
Relative Class ◽  
Relative Class Number

Explicit Upper Bounds for Residues of Dedekind Zeta Functions and Values of L-Functions at s = 1, and Explicit Lower Bounds for Relative Class Numbers of CM-Fields

2001 ◽  
Vol 53 (6) ◽  
pp. 1194-1222 ◽  
Author(s):  
Stéphane Louboutin
Keyword(s):  
Lower Bounds ◽  
Class Number ◽  
Zeta Functions ◽  
Number Fields ◽  
Upper Bounds ◽  
Class Numbers ◽  
Class Groups ◽  
Relative Class ◽  
Relative Class Number ◽  
Root Discriminants

AbstractWe provide the reader with a uniform approach for obtaining various useful explicit upper bounds on residues of Dedekind zeta functions of numbers fields and on absolute values of values at $s=1$ of $L$-series associated with primitive characters on ray class groups of number fields. To make it quite clear to the reader how useful such bounds are when dealing with class number problems for CM-fields, we deduce an upper bound for the root discriminants of the normal CM-fields with (relative) class number one.

Another look at real quadratic fields of relative class number 1

2014 ◽  
Vol 163 (4) ◽  
pp. 371-377 ◽  
Author(s):  
Debopam Chakraborty ◽  
Anupam Saikia
Keyword(s):  
Class Number ◽  
Quadratic Fields ◽  
Real Quadratic Fields ◽  
Relative Class ◽  
Relative Class Number ◽  
Real Quadratic

scholarly journals On Dirichletʼs conjecture on relative class number one

2012 ◽  
Vol 132 (7) ◽  
pp. 1398-1403 ◽  
Author(s):  
Amanda Furness ◽  
Adam E. Parker
Keyword(s):  
Class Number ◽  
Relative Class ◽  
Relative Class Number

A Generalization of Jakubec's Formula

2015 ◽  
Vol 65 (1) ◽  
Author(s):  
Mikihito Hirabayashi
Keyword(s):  
Class Number ◽  
Cyclotomic Field ◽  
Not Given ◽  
Relative Class ◽  
Relative Class Number

AbstractIn 2009 Jakubec gave two determinantal formulas for the relative class number of the pth cyclotomic field, p an odd prime. We generalize one of the formulas to an arbitrary cyclotomic field and also determine the sign of the formula, which he had not given.

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