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We consider the family of polynomials in of the form . Two such polynomials and are equivalent if there is an automorphism of such that . We give a complete classification of the equivalence classes of these polynomials in the algebraic and analytic category. As a consequence, we find the following results. There are explicit examples of inequivalent polynomials and such that the zero set of is isomorphic to the zero set of for all . There exist polynomials which are algebraically...
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