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 University Press

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
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