[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b150889

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)

Publication Information

Bulletin of the Korean Mathematical Society / v.53, no.6, 2016 , pp. 1697-1705 More about this Journal

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.

Keywords

linear isomorphisms; n-ary m-ic forms;

Citations & Related Records

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