Arithmetical Properties of Polynomials

The present article describes Erdős’s work contained in the following papers. [E1] On the coefficients of the cyclotomic polynomials, Bull. Amer. Math. Soc. 52 (1946), 179–183. [E2] On the coefficients of the cyclotomic polynomial, Portug. Math. 8 (1949), 63–71. [E3] On the number of terms of the square of a polynomial, Nieuw Archief voor Wiskunde (1949), 63–65. [E4] On the greatest prime factor of $$\mathop{\prod }\limits _{k=1}^{x}f(k)$$ , J. London Math. Soc. 27 (1952), 379–384. [E5] On the sum $$\sum \limits _{k=1}^{x}d(f(k))$$ , ibid. 7–15. [E6] Arithmetical properties of polynomials, ibid. 28 (1953), 436–425. [E7] Über arithmetische Eigenschaften der Substitutionswerte eines Polynoms für ganzzahlige Werte des Arguments, Revue Math. Pures et Appl. 1 (1956) No. 3, 189–194. [E8] On the growth of the cyclotomic polynomial in the interval (0,1), Proc. Glasgow Math. Assoc. 3 (1957), 102–104. [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). [E10] Bounds for the r-th coefficients of cyclotomic polynomials, J. London Math. Soc. (2) 8 (1974), 393–400 (with R. C. Vaughan). [E11] Prime polynomial sequences, ibid. (2) 14 (1976), 559–562 (with S. D. Cohen, M. B. Nathanson). [E12] On the greatest prime factor of $$\mathop{\prod }\limits _{k=1}^{x}f(k)$$ , Acta Arith. 55 (1990), 191–200 (with A. Schinzel).