Geodesic
A GENERALISED KUMMER'S CONJECTURE
Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 453-472

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DOI

Kummer's conjecture predicts the rate of growth of the relative class numbers of cyclotomic fields of prime conductor. We extend Kummer's conjecture to cyclotomic fields of conductor n, where n is any natural number. We show that the Elliott–Halberstam conjecture implies that this generalised Kummer's conjecture is true for almost all n but is false for infinitely many n.
DOI : 10.1017/S0017089510000340
Mots-clés : Primary 11R18, Secondary 11M20 
MYERS, M. J. R. A GENERALISED KUMMER'S CONJECTURE. Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 453-472. doi: 10.1017/S0017089510000340
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     title = {A {GENERALISED} {KUMMER'S} {CONJECTURE}},
     journal = {Glasgow mathematical journal},
     pages = {453--472},
     year = {2010},
     volume = {52},
     number = {3},
     doi = {10.1017/S0017089510000340},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000340/}
}
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