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Isolated minima of the product of n linear forms

Published online by Cambridge University Press:  24 October 2008

E. S. Barnes
E. S. Barnes
Affiliation:
Trinity CollegeCambridge
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Extract

Let

be n linear forms with real coefficients and determinant Δ = ∥ aij∥ ≠ 0; and denote by M(X) the lower bound of | X1X2 … Xn| over all integer sets (u) ≠ (0). It is well known that γn, the upper bound of M(X)/|Δ| over all sets of forms Xi, is finite, and the value of γn has been determined when n = 2 and n = 3.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 1 , January 1953 , pp. 59 - 62
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

REFERENCES

(1)Davenport, H. and Rogers, C. A.Diophantine inequalities with an infinity of solutions. Philos. Trans. A, 242 (1950), 311–44.Google Scholar
(2)Mahler, K.On lattice-points in n-dimensional star bodies. I. Proc. roy. Soc. A, 187 (1946), 151–87.Google Scholar