Infinite hilbert class field towers over cyclotomic fields

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
12 Downloads (Pure)


We use a result of Y. Furuta to show that for almost all positive integers m, the cyclotomic field Q2 pi im))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 Q2 pi im))for some pm0.3385 + o(1). These results have immediate applications to the divisibility properties of the class number of Q2 pi i/m).

Original languageEnglish
Pages (from-to)27-32
Number of pages6
JournalGlasgow Mathematical Journal
Issue number1
Publication statusPublished - Jan 2008

Bibliographical note

Copyright 2008 Cambridge University Press. Article originally published in Glasgow Mathematical Journal, Volume 50, Issue 1, pp. 27-32. The original article can be found at


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