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

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

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
@article{10_1017_S0017089510000340,
     author = {MYERS, M. J. R.},
     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/}
}
TY  - JOUR
AU  - MYERS, M. J. R.
TI  - A GENERALISED KUMMER'S CONJECTURE
JO  - Glasgow mathematical journal
PY  - 2010
SP  - 453
EP  - 472
VL  - 52
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000340/
DO  - 10.1017/S0017089510000340
ID  - 10_1017_S0017089510000340
ER  - 
%0 Journal Article
%A MYERS, M. J. R.
%T A GENERALISED KUMMER'S CONJECTURE
%J Glasgow mathematical journal
%D 2010
%P 453-472
%V 52
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000340/
%R 10.1017/S0017089510000340
%F 10_1017_S0017089510000340

[1] 1.Ankeny, N. C. and Chowla, S., The class number of the cyclotomic field. Canad. J. Math. 3 (1951), 486–494. Google Scholar | DOI

[2] 2.Apostol, T. M., Introduction to analytic number theory (Springer-Verlag, New York, 1995). Google Scholar

[3] 3.Granville, A., On the size of the first factor of the class number of a cyclotomic field, Invent. Math. 100 (1990), 321–338. Google Scholar | DOI

[4] 4.Halberstam, H. and Richert, H. E., Sieve methods (Academic Press, London, 1974). Google Scholar

[5] 5.Hardy, G. H. and Ramanujan, S., The normal number of prime factors of a number n, Q. J. Math. 48 (1917), 76–92. Google Scholar

[6] 6.Hooley, C., On the Brun–Titchmarsh theorem, II, Proc. Lond. Math. Soc. (3) 30 (1975), 114–128. Google Scholar | DOI

[7] 7.Kummer, E. E., Collected papers (Springer-Verlag, New York, 1975). Google Scholar

[8] 8.Lu, Y. and Zhang, W., On the Kummer conjecture, Acta Arith. 131 (2008), 87–102. Google Scholar | DOI

[9] 9.Murty, M. R. and Petridis, Y. N., On Kummer's conjecture, J. Number Theory 90 (2001), 294–303. Google Scholar | DOI

[10] 10.Myers, M. J. R., A prime power variation of Kummer's conjecture, J. Ramanujan Math. Soc. (submitted). Google Scholar

[11] 11.Washington, L. C., Introduction to cyclotomic fields (Springer-Verlag, New York, 1982). Google Scholar | DOI

Cité par Sources :