We develop an efficient technique for computing relative
class numbers of imaginary abelian fields, efficient enough
to enable us to easily compute relative class numbers of
imaginary cyclic fields of degrees $32$ and conductors
greater than $10^{13}$, or of degrees $4$ and conductors
greater than $10^{15}$. Acccording to our extensive
computation, all the $166204$ imaginary cyclic quartic
fields of prime conductors $p$ less than $10^7$ have relative
class numbers less than $p$/2. Our major innovation is a
technique for computing numerically root numbers appearing
in some functional equations.
Publié le : 1998-05-14
Classification:
Imaginary abelian number field,
relative class number,
11Y40,
11M20,
11R20,
11R29
@article{1047674147,
author = {Louboutin, St\'ephane},
title = {Computation of relative class numbers of imaginary abelian number fields},
journal = {Experiment. Math.},
volume = {7},
number = {4},
year = {1998},
pages = { 293-303},
language = {en},
url = {http://dml.mathdoc.fr/item/1047674147}
}
Louboutin, Stéphane. Computation of relative class numbers of imaginary abelian number fields. Experiment. Math., Tome 7 (1998) no. 4, pp. 293-303. http://gdmltest.u-ga.fr/item/1047674147/