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On the monogenity of polynomials with non-squarefree discriminants
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In 2012, for any integer n≥2, Kedlaya constructed an infinite class of monic irreducible polynomials of degree n with integer coefficients having squarefree discriminants. Such polynomials are necessarily monogenic. Further, by extending Kedlaya’s approach, for any odd prime q, Jones constructed a class of monogenic polynomials of degree q with non-squarefree discriminants. In this article, using a method similar to the one provided by Jones, we present another infinite class of monogenic polynomials of degree q with non-squarefree discriminants, where q is a prime of the form q=q0+q1−1, with q0 and q1 being prime numbers. In addition, we present a class of non-monogenic polynomials whose coefficients are Stirling numbers of the first kind.
Institute of Mathematics, Polish Academy of Sciences
Title: On the monogenity of polynomials with non-squarefree discriminants
Description:
In 2012, for any integer n≥2, Kedlaya constructed an infinite class of monic irreducible polynomials of degree n with integer coefficients having squarefree discriminants.
Such polynomials are necessarily monogenic.
Further, by extending Kedlaya’s approach, for any odd prime q, Jones constructed a class of monogenic polynomials of degree q with non-squarefree discriminants.
In this article, using a method similar to the one provided by Jones, we present another infinite class of monogenic polynomials of degree q with non-squarefree discriminants, where q is a prime of the form q=q0+q1−1, with q0 and q1 being prime numbers.
In addition, we present a class of non-monogenic polynomials whose coefficients are Stirling numbers of the first kind.
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