scholarly journals Class numbers of totally real fields and applications to the Weber class number problem

2014 ◽  
Vol 164 (4) ◽  
pp. 381-397 ◽  
Author(s):  
John C. Miller
Keyword(s):  
Class Number ◽  
Class Numbers ◽  
Number Problem ◽  
Totally Real ◽  
Totally Real Fields

scholarly journals Application of the Strong Artin Conjecture to the Class Number Problem

2013 ◽  
Vol 65 (6) ◽  
pp. 1201-1216 ◽  
Author(s):  
Peter J. Cho ◽  
Henry H. Kim
Keyword(s):  
Class Number ◽  
Number Fields ◽  
Class Numbers ◽  
Density Result ◽  
Class Number Formula ◽  
Number Problem ◽  
Number Formula ◽  
Group A ◽  
Galois Closures ◽  
Extremal Value

AbstractWe construct unconditionally several families of number fields with the largest possible class numbers. They are number fields of degree 4 and 5 whose Galois closures have the Galois group A4; S4, and S5. We first construct families of number fields with smallest regulators, and by using the strong Artin conjecture and applying the zero density result of Kowalski–Michel, we choose subfamilies of L-functions that are zero-free close to 1. For these subfamilies, the L-functions have the extremal value at s = 1, and by the class number formula, we obtain the extreme class numbers.

The determination of the class-numbers of totally real cubic fields

1961 ◽  
Vol 57 (4) ◽  
pp. 728-730 ◽  
Author(s):  
H. J. Godwin
Keyword(s):  
Class Number ◽  
Sum Of Squares ◽  
Class Numbers ◽  
Cubic Field ◽  
Cubic Fields ◽  
Totally Real

In a previous paper (2) it was shown how the work of finding the units of a totally real cubic field could be facilitated by consideration of the sum of squares of differences between a number and its conjugates. In the present paper it is shown that the same ideas can be helpful in the calculation of class-numbers, and a list of the fields with class-number greater than unity and discriminant less than 20,000 is given.

scholarly journals Λ-adic modular symbols over totally real fields

2011 ◽  
pp. 841-865 ◽  
Author(s):  
Baskar Balasubramanyam ◽  
Matteo Longo
Keyword(s):  
Modular Symbols ◽  
Totally Real ◽  
Totally Real Fields

scholarly journals Motives over totally real fields and $p$-adic $L$-functions

1994 ◽  
Vol 44 (4) ◽  
pp. 989-1023 ◽  
Author(s):  
Alexei A. Panchishkin
Keyword(s):  
Totally Real ◽  
Totally Real Fields
Sign in / Sign up

Export Citation Format

Share Document