Square-free values of cubic polynomials in algebraic number fields
نویسندگان
چکیده
منابع مشابه
Square-free Values of Reducible Polynomials
We calculate admissible values of r such that a square-free polynomial with integer coefficients, no fixed prime divisor and irreducible factors of degree at most 3 takes infinitely many values that are a product of at most r distinct primes.
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The algorithm for factoring polynomials over the integers by Wang and Rothschild is generalized to an algorithm for the irreducible factorization of multivariate polynomials over any given algebraic number field. The extended method makes use of recent ideas in factoring univariate polynomials over large finite fields due to Berlekamp and Zassenhaus. The procedure described has been implemented...
متن کاملFactoring Multivariate Polynomials over Algebraic Number Fields
The algorithm for factoring polynomials over the integers by Wang and Rothschild is generalized to an algorithm for the irreducible factorization of multivariate polynomials over any given algebraic number field. The extended method makes use of recent ideas in factoring univariate polynomials over large finite fields due to Berlekamp and Zassenhaus. The procedure described has been implemented...
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If f(x1, ..., xn) ∈ Z[x1, ..., xn] has the property that every integer specialization gives an integral square value, then f is itself the square of a polynomial. We also give an effective version of this result by using an effective version of a classical theorem of E. Noether along with a theorem of Lang and Weil.
متن کاملSquare-free values of polynomials over the rational function field
Article history: Received 23 August 2013 Accepted 23 August 2013 Available online xxxx Communicated by K. Soundararajan
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1989
ISSN: 0022-314X
DOI: 10.1016/0022-314x(89)90087-5