scholarly journals On the relative class number of finite algebraic number fields

1967 ◽  
Vol 19 (2) ◽  
pp. 179-184 ◽  
Author(s):  
Akio YOKOYAMA
Keyword(s):  
Algebraic Number ◽  
Class Number ◽  
Number Fields ◽  
Algebraic 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.

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