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Note on non-homogeneous 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 θ be an algebraic number of degree n, with conjugates θ(1), …, θ(n), where θ(1), …, θ(r) are real and θ(r+j), θ(r+s+j) are complex conjugates for j = 1, …, s. [Here r ≥ 0, s ≥ 0, r + 2s = n.] Let ω1, …, ωn be a basis for the integers of k(θ), and set

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 2 , April 1953 , pp. 360 - 362
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

REFERENCES

(1)Clarke, L. E.Non-homogeneous linear forms associated with algebraic fields. Quart. J. Math. (2), 2 (1951), 308–15.CrossRefGoogle Scholar
(2)Davenport, H.Linear forms associated with an algebraic number-field. Quart. J. Math. (2), 3 (1952), 32–41.CrossRefGoogle Scholar
(3)Hardy, G. H. and Weight, E. M.Theory of numbers (Oxford, 1945), pp. 396–8.Google Scholar