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Small Solutions of Congruences in a Large Number of Variables1

Published online by Cambridge University Press:  20 November 2018

Wolfgang M. Schmidt
Wolfgang M. Schmidt*
Affiliation:
University of Colorado Boulder, Colorado, U.S.A.
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Abstract

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It is shown that a system of congruences 1(x) ≡ . . . ≡

(x) = 0 (mod m)

where each i(x) = i,(x1, .. . ,x2,) is a form of degree at most k has a nontrivial solution x satisfying |xi|≦cm(½)+∊ (i=1,...,S)

with c = c(k,r,∊), provided that ∊ > 0 and that S > S1(k,r,∊).

Keywords

10B3010C10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 3 , 01 September 1985 , pp. 295 - 305
Copyright
Copyright © Canadian Mathematical Society 1985

Footnotes

1

Written with partial support from NSF-MCS-8211461.

References

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