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Some new polynomial discriminant formulas

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Abstract

We generalize recent discriminant formulas of the second author, and we give discriminant formulas for some classes of irreducible polynomials found by the first author. In addition, we find other classes of irreducible polynomials, and we provide discriminant formulas for them as well.

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References

  1. D.W. Boyd, G. Martin, and M. Thom, Squarefree values of trinomial discriminants, LMS J. Comput. Math., 18(1): 148–169, 2015.

    Article  MathSciNet  Google Scholar 

  2. K. Dilcher and K.B. Stolarsky, Resultants and discriminants of Chebyshev and related polynomials, Trans. Am. Math. Soc., 357(3):965–981, 2005.

    Article  MathSciNet  Google Scholar 

  3. M. Filaseta, Rouché’s theorem for polynomials, Am. Math. Mon., 97(9):834–835, 1990.

    MATH  Google Scholar 

  4. T.A. Gassert, Discriminants of Chebyshev radical extensions, J. Théor. Nombres Bordx., 26(3):607–634, 2014.

    Article  MathSciNet  Google Scholar 

  5. T.A. Gassert, A note on the monogeneity of power maps, Albanian J. Math., 11(1):3–12, 2017.

    MathSciNet  MATH  Google Scholar 

  6. J. Harrington, On the factorization of the trinomials xn +cxn−1+d, Int. J. Number Theory, 8(6):1513–1518, 2012.

    Article  MathSciNet  Google Scholar 

  7. J. Harrington and L. Jones, Monogenic binomial compositions, Taiwanese J. Math., 24(5):1073–1090, 2020.

    Article  MathSciNet  Google Scholar 

  8. J. Harrington and L. Jones, Monogenic cyclotomic compositions, Kodai Math. J., 44(1):11—125, 2021.

    Article  MathSciNet  Google Scholar 

  9. K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, 2nd ed., Grad. Texts Math., Vol. 84, Springer, New York, 1990.

  10. L. Jones, A brief note on some infinite families of monogenic polynomials, Bull. Aust. Math. Soc., 100(2):239–244, 2019.

    Article  MathSciNet  Google Scholar 

  11. L. Jones, Monogenic polynomials with non-squarefree discriminant, Proc. Am. Math. Soc., 148(4):1527–1533, 2020.

    Article  MathSciNet  Google Scholar 

  12. L. Jones, Some new infinite families of monogenic polynomials with non-squarefree discriminant, Acta Arith., 197(2):213–219, 2021.

    Article  MathSciNet  Google Scholar 

  13. L. Jones and T. Phillips, Infinite families of monogenic trinomials and their Galois groups, Int. J. Math., 29(5): 1850039, 2018.

    Article  MathSciNet  Google Scholar 

  14. K. Kedlaya, A construction of polynomials with squarefree discriminants, Proc. Am. Math. Soc., 140(9):3025–3033, 2012.

    Article  MathSciNet  Google Scholar 

  15. O. Perron, Neue Kriterien für die Irreduzibilität algebraischer Gleichungen, J. Reine Angew. Math., 132:288–307, 1907 (in German).

    MathSciNet  MATH  Google Scholar 

  16. R. Swan, Factorization of polynomials over finite fields, Pacific J. Math., 12:1099–1106, 1962.

    Article  MathSciNet  Google Scholar 

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Correspondence to Lenny Jones.

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Harrington, J., Jones, L. Some new polynomial discriminant formulas. Lith Math J 61, 483–490 (2021). https://doi.org/10.1007/s10986-021-09540-x

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  • DOI: https://doi.org/10.1007/s10986-021-09540-x

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