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The distribution of the irreducibles in an algebraic number field

Published online by Cambridge University Press:  09 April 2009

David M. Bradley
Affiliation:
Department of Mathematics and Statistics, University of Maine, Orono, Maine 04469, USA, e-mail: [email protected], [email protected], [email protected]
Ali E. Özlük
Affiliation:
19 Balsam Drive, Bangor, Maine 04401, USA, e-mail: [email protected]
Rebecca A. Rozario
Affiliation:
19 Balsam Drive, Bangor, Maine 04401, USA, e-mail: [email protected]
C. Snyder
Affiliation:
19 Balsam Drive, Bangor, Maine 04401, USA, e-mail: [email protected]
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Abstract

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We study the distribution of principal ideals generated by irreducible elements in an algebraic number field.

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Bradley, D. M., Özlük, A. E. and Snyder, C., ‘On a class number formula for real quadratic number fields’, Bull. Austral. Math. Soc. 65 (2002), 259270.CrossRefGoogle Scholar
[2]Dummit, D. S. and Foote, R. M., Abstract algebra, 2nd edition (Prentice Hall, Upper Saddle River, NJ, 1999).Google Scholar
[3]Gao, W. D., ‘The structure of two classes of sequences in Z n’, Adv. in Math. (China) 22 (1993), 348353.Google Scholar
[4]Gradshteyn, I. S. and Ryzhik, I. M., Table of integrals, series, and products, 5th edition (Academic Presss, Boston, 1994).Google Scholar
[5]Halter-Kocha, F. and Müller, W., ‘Quantitative aspects of non-unique factoriztion; A general theory with applications to algebraic function fields’, J. Reine Angew. Math. 421 (1991), 159188.Google Scholar
[6]Kaczorowski, J., ‘Some remarks on factorization in algebraic number fields’, Acta Arith. 43 (1983), 5368.CrossRefGoogle Scholar
[7]Landau, E., Einführung in die elementare und analytische Theorie der algebraischen Zahlen und der Ideale (Chelsea Pub. Co., New York, 1949).Google Scholar
[8]Lang, S., Algebraic number theory (Addison-Wesley, London, 1970).Google Scholar
[9]Lammermeyer, F., ‘Kuroda's class number formula’, Acta Arith. 66 (1994), 245260.CrossRefGoogle Scholar
[10]Lemmermeyer, F., ‘Ideal class groups of cyclotomic number fields I’, Acta Arith. 72 (1995), 347359.CrossRefGoogle Scholar
[11]Rémond, J. P., ‘Étude asymptotique de certaines partitions dans certaines semi-groups’, Ann. Sci. École Norm. Sup. 83 (1966), 343410.CrossRefGoogle Scholar
[12]Washington, L., Introduction to cyclotomic fields (Springer, New York, 1982).CrossRefGoogle Scholar
[13]Wrench, J. W. Jr,‘Concerning two series for the gamma function’, Math. Comp. 22 (1968), 617626.CrossRefGoogle Scholar