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On the product of n linear forms

Published online by Cambridge University Press:  24 October 2008

H. Davenport
H. Davenport
Affiliation:
University CollegeGower StreetLondon, W.C.1
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Extract

Let L1, …, Ln be n homogeneous linear forms in n variables u1, …, un, with non-zero determinant Δ. Suppose that L1, …, Lr have real coefficients, that Lr+1, …, Lr+s have complex coefficients, and that the form Lr+s+j is the complex conjugate of the form Lr+j for j = 1, …, s, where r + 2s = n. Let

for integral u1, …, un, not all zero. For any n numbers α1, …, αn of the same ‘type’ as the forms L1, …, Ln (that is, α1, …, αr real, αr+1, …, αr+s complex, αr+s+j = ᾱr+j), let

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 2 , April 1953 , pp. 190 - 193
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

REFERENCES

(1)Barnes, E. S.Proc. Camb. phil. Soc. 49 (1953), 360–2.CrossRefGoogle Scholar
(2)Cassels, J. W. S.J. Lond. math. Soc. 27 (1952), 485–92.CrossRefGoogle Scholar
(3)Davenport, H.Quart. J. Math. (2), 3 (1952), 32–41.CrossRefGoogle Scholar