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The inhomogeneous minimum of binary quadratic, ternary cubic and quaternary quartic forms

Published online by Cambridge University Press:  24 October 2008

J. W. S. Cassels
J. W. S. Cassels
Affiliation:
Trinity CollegeCambridge
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Extract

In this paper I prove the following results.

Theorem 1. Let f(x, y) = ax2 + bxy + cy2be an indefinite form. Then there exist real (x0, y0) such that

for all (x, y) ≡ (x0, y0) (mod 1). If f represents 0 there are indenumerably many such incongruent (x0, y0).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 48 , Issue 1 , January 1952 , pp. 72 - 86
Copyright
Copyright © Cambridge Philosophical Society 1952

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References

REFERENCES

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