Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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LINEAR ISOMORPHISMS OF NON-DEGENERATE INTEGRAL TERNARY CUBIC FORMS

  • Lee, Inhwan (Department of Mathematical Sciences Seoul National University) ;
  • Oh, Byeong-Kweon (Department of Mathematical Sciences and Research Institute of Mathematics Seoul National University)
  • Received : 2015.10.29
  • Published : 2016.11.30
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Abstract

In this article, we consider the problem on finding non-degenerate nary m-ic forms having an $n{\times}n$ matrix A as a linear isomorphism. We show that it is equivalent to solve a linear diophantine equation. In particular, we find all integral ternary cubic forms having A as a linear isomorphism, for any $A{\in}GL_3({\mathbb{Z}})$. We also give a family of non-degenerate cubic forms F such that F(x) = N always has infinitely many integer solutions if exists.

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References

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