Acta Mathematica Sinica

, Volume 9, Issue 4, pp 382–389

On small zeros of quadratic forms over finite fields (II)

  • Wang Yuan
Article

DOI: 10.1007/BF02560131

Cite this article as:
Yuan, W. Acta Mathematica Sinica (1993) 9: 382. doi:10.1007/BF02560131
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Abstract

Let\(Q(\underline{\underline x} ) = Q(x_1 , \cdot \cdot \cdot x_n )\) be a quadratic form with integer coefficients and letp denote a prime. Cochrane[1] proved that ifn≥4 then\(Q(\underline{\underline x} ) = 0(\bmod p)\) has a solution\(\underline{\underline x} \ne \underline{\underline 0} \) satisfying\(\left| {\underline{\underline x} } \right| \ll \sqrt p \), where\(\left| {\underline{\underline x} } \right| = \max \left| {x_i } \right|\). The aim of the present paper is to generalize the above result to finite fields.

Copyright information

© Science Press 1993

Authors and Affiliations

  • Wang Yuan
    • 1
  1. 1.Institute of MathematicsAcademia SinicaBeijingChina

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