Geodesic
On Cyclic Fields of Odd Prime Degree p with Infinite Hilbert p-Class Field Towers
Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 86-88

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DOI

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.
DOI : 10.4153/CMB-2002-009-8
Mots-clés : 11R29, 11R37, 11R45 
III, Frank Gerth. On Cyclic Fields of Odd Prime Degree p with Infinite Hilbert p-Class Field Towers. Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 86-88. doi: 10.4153/CMB-2002-009-8
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     author = {III, Frank Gerth},
     title = {On {Cyclic} {Fields} of {Odd} {Prime} {Degree} p with {Infinite} {Hilbert} {p-Class} {Field} {Towers}},
     journal = {Canadian mathematical bulletin},
     pages = {86--88},
     year = {2002},
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     doi = {10.4153/CMB-2002-009-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-009-8/}
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