Abstract view
On Cyclic Fields of Odd Prime Degree $p$ with Infinite Hilbert $p$Class Field Towers


Published:20020301
Printed: Mar 2002
Abstract
Let $k$ be a cyclic extension of odd prime degree $p$ of the field of
rational numbers. If $t$ denotes the number of primes that ramify in $k$,
it is known that the Hilbert $p$class field tower of $k$ is infinite if
$t>3+2\sqrt p$. For each $t>2+\sqrt p$, this paper shows that a positive
proportion of such fields $k$ have infinite Hilbert $p$class field towers.