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Inequalities for ideal bases in algebraic number fields

Published online by Cambridge University Press:  09 April 2009

K. Mahler
K. Mahler
Affiliation:
Mathematics Department, Institute of Advanced Studies, Australian National University, Canberra, A.C.T., 28 April, 1964.
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In a paper of nearly thirty years ago (Mahler 1937) I first studied approximation properties of algebraic number fields relative to their full system of inequivalent valuations. I now return to these questions with a slightly improved method and establish a number of existence theorems for such fields.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 4 , November 1964 , pp. 425 - 448
Copyright
Copyright © Australian Mathematical Society 1964

References

Artin, E., 1959, Theory of algebraic numbers, Mathematisches Institut, Göttingen.Google Scholar
Artin, E. & Whaples, G., 1945, Bull. Am. Math. Soc. 51, 469–492.CrossRefGoogle Scholar
Cassels, J. W. S., 1959, An introduction to the geometry of numbers, Springer-Verlag, Berlin.CrossRefGoogle Scholar
Hasse, H., 1963, Zahlentheorie, Akademie-Verlag, Berlin.CrossRefGoogle Scholar
Lang, S., 1964, Algebraic numbers, Addison-Wesley Publishing Co., Reading, Mass.Google Scholar
Mahler, K., 1937, Acta Mathematica 68, 109–144.CrossRefGoogle Scholar
Mahler, K., 1938, Proc. Koninkl. Akad. Wetensch. Amsterdam, 41, 634–637.Google Scholar
O'Meara, O. T., 1963, Introduction to quadratic forms, Springer Verlag, Berlin.CrossRefGoogle Scholar
Minkowski, H., 1899, Nachr. Ges. Wiss. Göttingen, 64–66.Google Scholar
Waerden, B. L. v. d., 1956, Acta Mathematica 96, 265–309.CrossRefGoogle Scholar
Weyl, H., 1942, Proc. London Math. Soc. 47, 268–289.CrossRefGoogle Scholar