Geodesic
NOTE ON THE DIVISIBILITY OF THE CLASS NUMBER OF CERTAIN IMAGINARY QUADRATIC FIELDS
Glasgow mathematical journal, Tome 51 (2009) no. 1, pp. 187-191

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

We prove that the class number of the imaginary quadratic field is divisible by n for any positive integers k and n with 22k < 3n, by using Y. Bugeaud and T. N. Shorey's result on Diophantine equations.
DOI : 10.1017/S001708950800462X
Mots-clés : 11R11, 11R29 
KISHI, YASUHIRO. NOTE ON THE DIVISIBILITY OF THE CLASS NUMBER OF CERTAIN IMAGINARY QUADRATIC FIELDS. Glasgow mathematical journal, Tome 51 (2009) no. 1, pp. 187-191. doi: 10.1017/S001708950800462X
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[1] 1.Ankeny, N. C. and Chowla, S., On the divisibility of the class number of quadratic fields, Pacific J. Math. 5 (1955), 321–324. Google Scholar | DOI

[2] 2.Bugeaud, Y. and Shorey, T. N., On the number of solutions of the generalized Ramanujan-Nagell equation, J. Reine Angew. Math. 539 (2001), 55–74. Google Scholar

[3] 3.Gross, B. H. and Rohrlich, D. E., Some results on the Mordell-Weil group of the Jacobian of the Fermat curve, Invent. Math. 44 (1978), 201–224. Google Scholar | DOI

[4] 4.Herschfeld, A., The equation 2x − 3y = d, Bull. Amer. Math. Soc. 42 (1936), 231–234. Google Scholar | DOI

[5] 5.Ichimura, H., Note on the class numbers of certain real quadratic fields, Abh. Math. Sem. Univ. Hamburg 73 (2003), 281–288. Google Scholar | DOI

[6] 6.Mollin, R. A., Solutions of Diophantine equations and divisibility of class numbers of complex quadratic fields, Glasgow Math. J. 38 (1996), 195–197. Google Scholar | DOI

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