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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Small solutions of cubic congruences


Author: Todd Cochrane
Journal: Proc. Amer. Math. Soc. 106 (1989), 333-334
MSC: Primary 11D79; Secondary 11D25
MathSciNet review: 964454
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Abstract: Let $ C({\mathbf{x}})$ be a cubic form in $ n$ variables over $ {\mathbf{Z}}$ and $ p$ be a prime. Then for $ 0 < \sigma < \frac{2}{3}$ the congruence $ C({\mathbf{x}}) \equiv 0(\bmod p)$ has a nonzero solution $ x$ with $ \max \left\vert {{x_i}} \right\vert \ll {p^{1/3 + \sigma }}$, provided that $ n > 8/\sigma $, (where the constant in the $ \ll $ depends on $ n$ and $ \sigma $).


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0964454-X
PII: S 0002-9939(1989)0964454-X
Article copyright: © Copyright 1989 American Mathematical Society