Arithmetical Properties of Polynomials



The present article describes Erdős’s work contained in the following papers.
  1. [E1]

    On the coefficients of the cyclotomic polynomials, Bull. Amer. Math. Soc. 52 (1946), 179–183.

  2. [E2]

    On the coefficients of the cyclotomic polynomial, Portug. Math. 8 (1949), 63–71.

  3. [E3]

    On the number of terms of the square of a polynomial, Nieuw Archief voor Wiskunde (1949), 63–65.

  4. [E4]

    On the greatest prime factor of \(\mathop{\prod }\limits _{k=1}^{x}f(k)\), J. London Math. Soc. 27 (1952), 379–384.

  5. [E5]

    On the sum \(\sum \limits _{k=1}^{x}d(f(k))\), ibid. 7–15.

  6. [E6]

    Arithmetical properties of polynomials, ibid. 28 (1953), 436–425.

  7. [E7]

    Über arithmetische Eigenschaften der Substitutionswerte eines Polynoms für ganzzahlige Werte des Arguments, Revue Math. Pures et Appl. 1 (1956) No. 3, 189–194.

  8. [E8]

    On the growth of the cyclotomic polynomial in the interval (0,1), Proc. Glasgow Math. Assoc. 3 (1957), 102–104.

  9. [E9]

    On the product \(\mathop{\prod }\limits _{k=1}^{n}(1 {-\zeta }^{a_{i}})\), Publ. Inst. Math. Beograd 13 (1959), 29–34 (with G. Szekeres).

  10. [E10]

    Bounds for the r-th coefficients of cyclotomic polynomials, J. London Math. Soc. (2) 8 (1974), 393–400 (with R. C. Vaughan).

  11. [E11]

    Prime polynomial sequences, ibid. (2) 14 (1976), 559–562 (with S. D. Cohen, M. B. Nathanson).

  12. [E12]

    On the greatest prime factor of \(\mathop{\prod }\limits _{k=1}^{x}f(k)\), Acta Arith. 55 (1990), 191–200 (with A. Schinzel).



London Math Asymptotic Formula Absolute Constant Multiplicative Function Irreducible Polynomial 
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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute of MathematicsPolish Academy of SciencesWarsawPoland

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