Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T07:17:42.931Z Has data issue: false hasContentIssue false
  • English
  • Français

The distribution of the irreducibles in an algebraic number field

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  09 April 2009

David M. Bradley ,
Ali E. Özlük ,
Rebecca A. Rozario  and
C. Snyder
David M. Bradley
Affiliation:
Department of Mathematics and Statistics, University of Maine, Orono, Maine 04469, USA, e-mail: Bradley@math.umaine.edu, ozluk@math.umaine.edu, snyder@math.umaine.edu
Ali E. Özlük
Affiliation:
19 Balsam Drive, Bangor, Maine 04401, USA, e-mail: rebecca.rozario@umit.edu
Rebecca A. Rozario
Affiliation:
19 Balsam Drive, Bangor, Maine 04401, USA, e-mail: rebecca.rozario@umit.edu
C. Snyder
Affiliation:
19 Balsam Drive, Bangor, Maine 04401, USA, e-mail: rebecca.rozario@umit.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

MSC classification

Secondary: 11R27: Units and factorization
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 3 , December 2005 , pp. 369 - 390
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), 259–270.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), 348–353.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), 159–188.Google Scholar
[6]Kaczorowski, J., ‘Some remarks on factorization in algebraic number fields’, Acta Arith. 43 (1983), 53–68.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), 245–260.CrossRefGoogle Scholar
[10]Lemmermeyer, F., ‘Ideal class groups of cyclotomic number fields I’, Acta Arith. 72 (1995), 347–359.CrossRefGoogle Scholar
[11]Rémond, J. P., ‘Étude asymptotique de certaines partitions dans certaines semi-groups’, Ann. Sci. École Norm. Sup. 83 (1966), 343–410.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), 617–626.CrossRefGoogle Scholar