On the class numbers of real cyclotomic fields of conductor pq

Eleni Agathocleous. "On the class numbers of real cyclotomic fields of conductor pq." Acta Arithmetica 165.3 (2014): 257-277. <http://eudml.org/doc/278854>.

@article{EleniAgathocleous2014,
abstract = {The class numbers h⁺ of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows, and methods employing Leopoldt's decomposition of the class number become hard to use when the field extension is not cyclic of prime power. This is why other methods have been developed, which approach the problem from different angles. In this paper we extend one of these methods that was designed for real cyclotomic fields of prime conductor, and we make it applicable to real cyclotomic fields of conductor equal to the product of two distinct odd primes. The main advantage of this method is that it does not exclude the primes dividing the order of the Galois group, in contrast to other methods. We applied our algorithm to real cyclotomic fields of conductor < 2000 and we calculated the full order of the l-part of h⁺ for all odd primes l < 10000.},
author = {Eleni Agathocleous},
journal = {Acta Arithmetica},
keywords = {computation of class numbers; real cyclotomic fields; non-prime conductor},
language = {eng},
number = {3},
pages = {257-277},
title = {On the class numbers of real cyclotomic fields of conductor pq},
url = {http://eudml.org/doc/278854},
volume = {165},
year = {2014},
}

TY - JOUR
AU - Eleni Agathocleous
TI - On the class numbers of real cyclotomic fields of conductor pq
JO - Acta Arithmetica
PY - 2014
VL - 165
IS - 3
SP - 257
EP - 277
AB - The class numbers h⁺ of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows, and methods employing Leopoldt's decomposition of the class number become hard to use when the field extension is not cyclic of prime power. This is why other methods have been developed, which approach the problem from different angles. In this paper we extend one of these methods that was designed for real cyclotomic fields of prime conductor, and we make it applicable to real cyclotomic fields of conductor equal to the product of two distinct odd primes. The main advantage of this method is that it does not exclude the primes dividing the order of the Galois group, in contrast to other methods. We applied our algorithm to real cyclotomic fields of conductor < 2000 and we calculated the full order of the l-part of h⁺ for all odd primes l < 10000.
LA - eng
KW - computation of class numbers; real cyclotomic fields; non-prime conductor
UR - http://eudml.org/doc/278854
ER -