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On the inhomogeneous minimum of the product of n linear forms

Published online by Cambridge University Press:  26 February 2010

B. J. Birch  and
H. P. F. Swinnerton-Dyer
B. J. Birch
Affiliation:
Trinity College, Cambridge.
H. P. F. Swinnerton-Dyer
Affiliation:
Trinity College, Cambridge.
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Extract

The following well-known conjecture is generally attributed to Minkowski:

Let L1, …, Ln be n real homogeneous linear forms of determinant Δ ≠ 0 in the n variables x1, …, xn; and let (x1′, …, xn′) be any point. Then there exists a point (x1, xn) congruent to (x1′, …, xn′) (mod 1) at which

Type
Research Article
Information
Mathematika , Volume 3 , Issue 1 , June 1956 , pp. 25 - 39
Copyright
Copyright © University College London 1956

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References

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