Electronic Resource
Springer
Monatshefte für Mathematik
86 (1979), S. 285-300
ISSN:
1436-5081
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract An important problem in the field of Diophantine Approximation was solved in 1891 byHurwitz. He could show that any irrational number can be approximated by infinitely many rationals in such a way that the modulus of the difference multiplied with the square of the denominator is less than 5−1/2, and there 5−1/2 is best possible.-The generalization of this problem in the direction of simultaneous Diophantine Approximation is still unsolved.Furtwängler in 1925 gave lower bounds for the maximum difference, conjecturing that these were best possible.-Here it is shown that in the two dimensional caseFurtwängler's bounds are indeed best possible for certain irrationals lying in cubic number fields which are not totally real. Yet by considering totally real cubic fields we are led to replaceFurtwängler's conjecture by a new one.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01300244
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