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Published in:
2013 | OriginalPaper | Chapter
Arithmetical Properties of Polynomials
Author : Andrzej Schinzel
Published in: The Mathematics of Paul Erdős I
Publisher: Springer New York
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Abstract
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).