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

@article{JohnC2014,
abstract = {The determination of the class number of totally real fields of large discriminant is known to be a difficult problem. The Minkowski bound is too large to be useful, and the root discriminant of the field can be too large to be treated by Odlyzko's discriminant bounds. We describe a new technique for determining the class number of such fields, allowing us to attack the class number problem for a large class of number fields not treatable by previously known methods. We give an application to Weber's class number problem, which is the conjecture that all real cyclotomic fields of power of 2 conductor have class number 1.},
author = {John C. Miller},
journal = {Acta Arithmetica},
keywords = {class number; totally real field; cyclotomic field; Weber class number problem},
language = {eng},
number = {4},
pages = {381-397},
title = {Class numbers of totally real fields and applications to the Weber class number problem},
url = {http://eudml.org/doc/286225},
volume = {164},
year = {2014},
}

TY - JOUR
AU - John C. Miller
TI - Class numbers of totally real fields and applications to the Weber class number problem
JO - Acta Arithmetica
PY - 2014
VL - 164
IS - 4
SP - 381
EP - 397
AB - The determination of the class number of totally real fields of large discriminant is known to be a difficult problem. The Minkowski bound is too large to be useful, and the root discriminant of the field can be too large to be treated by Odlyzko's discriminant bounds. We describe a new technique for determining the class number of such fields, allowing us to attack the class number problem for a large class of number fields not treatable by previously known methods. We give an application to Weber's class number problem, which is the conjecture that all real cyclotomic fields of power of 2 conductor have class number 1.
LA - eng
KW - class number; totally real field; cyclotomic field; Weber class number problem
UR - http://eudml.org/doc/286225
ER -