Geodesic
Asymptotic Results for Class Number Divisibility in Cyclotomic Fields
Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 464-472

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DOI

Let n ≥3 and m≥3 be integers. Let Kn be the cyclotomic field obtained by adjoining a primitive nth root of unity to the field of rational numbers. Let denote the maximal real subfield of Kn . Let hn (resp., ) denote the class number of Kn (resp., ). For fixed m we show that m divides hn and hn for asymptotically almost all n. Also for those Kn and with a given number of ramified primes, we obtain lower bounds for certain types of densities for m dividing hn and .
DOI : 10.4153/CMB-1983-075-3
Mots-clés : 12A35, 12A50, 12A75 
III, Frank Gerth. Asymptotic Results for Class Number Divisibility in Cyclotomic Fields. Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 464-472. doi: 10.4153/CMB-1983-075-3
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     title = {Asymptotic {Results} for {Class} {Number} {Divisibility} in {Cyclotomic} {Fields}},
     journal = {Canadian mathematical bulletin},
     pages = {464--472},
     year = {1983},
     volume = {26},
     number = {4},
     doi = {10.4153/CMB-1983-075-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-075-3/}
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