Geodesic
INFINITE HILBERT CLASS FIELD TOWERS OVER CYCLOTOMIC FIELDS
Glasgow mathematical journal, Tome 50 (2008) no. 1, pp. 27-32

Voir la notice de l'article provenant de la source Cambridge

DOI

We use a result of Y. Furuta to show that for almost all positive integers m, the cyclotomic field has an infinite Hilbert p-class field tower with high rank Galois groups at each step, simultaneously for all primes p of size up to about (log logm)1 + o(1). We also use a recent result of B. Schmidt to show that for infinitely many m there is an infinite Hilbert p-class field tower over for some p≥m0.3385 + o(1). These results have immediate applications to the divisibility properties of the class number of .
DOI : 10.1017/S0017089507003977
Mots-clés : 11N25, 11R17, 11R37 
SHPARLINSKI, IGOR E. INFINITE HILBERT CLASS FIELD TOWERS OVER CYCLOTOMIC FIELDS. Glasgow mathematical journal, Tome 50 (2008) no. 1, pp. 27-32. doi: 10.1017/S0017089507003977
@article{10_1017_S0017089507003977,
     author = {SHPARLINSKI, IGOR E.},
     title = {INFINITE {HILBERT} {CLASS} {FIELD} {TOWERS} {OVER} {CYCLOTOMIC} {FIELDS}},
     journal = {Glasgow mathematical journal},
     pages = {27--32},
     year = {2008},
     volume = {50},
     number = {1},
     doi = {10.1017/S0017089507003977},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003977/}
}
TY  - JOUR
AU  - SHPARLINSKI, IGOR E.
TI  - INFINITE HILBERT CLASS FIELD TOWERS OVER CYCLOTOMIC FIELDS
JO  - Glasgow mathematical journal
PY  - 2008
SP  - 27
EP  - 32
VL  - 50
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003977/
DO  - 10.1017/S0017089507003977
ID  - 10_1017_S0017089507003977
ER  - 
%0 Journal Article
%A SHPARLINSKI, IGOR E.
%T INFINITE HILBERT CLASS FIELD TOWERS OVER CYCLOTOMIC FIELDS
%J Glasgow mathematical journal
%D 2008
%P 27-32
%V 50
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003977/
%R 10.1017/S0017089507003977
%F 10_1017_S0017089507003977

Cité par Sources :