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Generalized Maillet determinant

Published online by Cambridge University Press:  22 January 2016

S. Okada
S. Okada*
Affiliation:
Department of Mathematics, Faculty of Science Nagoya University, Chikusa-ku, Nagoya 464, Japan
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In this paper, we shall study a generalization of the Maillet determinant. hetp be an odd prime, and G = (Z/pZ)*. We shall identify any integer and its image in G if there is no fear of confusion. For any integer a, let R(a) denote an integer satisfying

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 94 , June 1984 , pp. 165 - 170
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

[ 1 ] Carlitz, L. and Olson, F. R., Maillet’s determinant, Proc. Amer. Math. Soc, 6 (1955), 265–269.Google Scholar
[ 2 ] Carlitz, L., A generalization of Maillet’s determinant and a bound for the first factor of the class number, Proc. Amer. Math. Soc, 12 (1961), 256–261.Google Scholar
[ 3 ] Lang, S., Cyclotomic Fields, Springer-Verlag, G.T.M., 1978.Google Scholar
[ 4 ] Iwasawa, K., A class number formula for cyclotomic fields, Ann. of Math., 76 (1962), 171–179.Google Scholar