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

Voir la notice de l'article provenant de la source Cambridge University Press

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
@article{10_4153_CMB_1983_075_3,
     author = {III, Frank Gerth},
     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/}
}
TY  - JOUR
AU  - III, Frank Gerth
TI  - Asymptotic Results for Class Number Divisibility in Cyclotomic Fields
JO  - Canadian mathematical bulletin
PY  - 1983
SP  - 464
EP  - 472
VL  - 26
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-075-3/
DO  - 10.4153/CMB-1983-075-3
ID  - 10_4153_CMB_1983_075_3
ER  - 
%0 Journal Article
%A III, Frank Gerth
%T Asymptotic Results for Class Number Divisibility in Cyclotomic Fields
%J Canadian mathematical bulletin
%D 1983
%P 464-472
%V 26
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-075-3/
%R 10.4153/CMB-1983-075-3
%F 10_4153_CMB_1983_075_3

[1] 1. Cornell, G. and Rosen, M., The l-rank of the real class group of cyclotomic fields, Abstracts Amer. Math. Soc, 3 (1982), 226. Google Scholar

[2] 2. Cornell, G. and Washington, L., Class numbers of cyclotomic fields, to appear. Google Scholar

[3] 3. Gerth, F. and Graham, S., Counting certain number fields with l-class number 1 or I, to appear. Google Scholar

[4] 4. Gerth, F., Counting certain number fields with prescribed l-class numbers, to appear in J. Reine Angew. Math. Google Scholar

[5] 5. Halberstam, H. and Richert, H.-E., Sieve Methods, Academic Press, London, 1974. Google Scholar

Cité par Sources :