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Approximation in algebraic function fields of one variable

Published online by Cambridge University Press:  09 April 2009

John Coates
John Coates
Affiliation:
Australian National UniversityCanberra, A.C.T
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In his paper (4), Mahler established several strong quantitative results on approximation in algebraic number fields using the geometry of numbers. In the present paper I derive analogous results for algebraic function fields of one variable using an analogue of the geometry of numbers.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 3 , August 1967 , pp. 341 - 355
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Artin, E., Algebraic numbers and algebraic functions (Princeton University, 1951).Google Scholar
[2]Hasse, H., Zahlentheorie (Akademie-Verlag, Berlin, 1963).CrossRefGoogle Scholar
[3]Lang, S., ‘Introduction to algebraic geometry’ (Interscience, New York, 1958).Google Scholar
[4]Mahler, K., ‘Inequalities for ideal bases in algebraic number fields’, J. Aust. Math. Soc. 4 (1964), 425–448.CrossRefGoogle Scholar
[5]Mahler, K., ‘Analogue of Minkowski's geometry of numbers in fields of series’, Ann. of Math., 42 (1941), 488–522.CrossRefGoogle Scholar
[6]O'Meara, O., Introduction to quadratic forms (Springer-Verlag, Berlin, 1963).CrossRefGoogle Scholar