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Displaying similar documents to “Algebraically solvable problems: describing polynomials as equivalent to explicit solutions.”

The set of points at which a polynomial map is not proper

Zbigniew Jelonek (1993)

Annales Polonici Mathematici

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We describe the set of points over which a dominant polynomial map f = ( f 1 , . . . , f n ) : ℂ n → ℂ n is not a local analytic covering. We show that this set is either empty or it is a uniruled hypersurface of degree bounded by ( ∏ i = 1 n d e g f i - μ ( f ) ) / ( m i n i = 1 , . . . , n d e g f i ) .

Comments on the height reducing property

Shigeki Akiyama, Toufik Zaimi (2013)

Open Mathematics

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A complex number α is said to satisfy the height reducing property if there is a finite subset, say F, of the ring ℤ of the rational integers such that ℤ[α] = F[α]. This property has been considered by several authors, especially in contexts related to self affine tilings and expansions of real numbers in non-integer bases. We prove that a number satisfying the height reducing property, is an algebraic number whose conjugates, over the field of the rationals, are all of modulus one,...

Quasi-permutation polynomials

Vichian Laohakosol, Suphawan Janphaisaeng (2010)

Czechoslovak Mathematical Journal

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A quasi-permutation polynomial is a polynomial which is a bijection from one subset of a finite field onto another with the same number of elements. This is a natural generalization of the familiar permutation polynomials. Basic properties of quasi-permutation polynomials are derived. General criteria for a quasi-permutation polynomial extending the well-known Hermite's criterion for permutation polynomials as well as a number of other criteria depending on the permuted domain and range...