Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 27, No. 2, pp. 211-221 (2011)

A factorization theorem for generalized exponential polynomyals with infinitely many integer zeros

Ouamporn Phuksuwan and Vichian Laohakosol

Chulalongkorn University, Kasetsart University

Abstract: A factorization theorem is proved for a class of generalized exponential polynomials having all but finitely many of integer zeros belong to a finite union of arithmetic progressions. This theorem extends a similar result for ordinary exponential polynomials due to H. N. Shapiro in 1959. The factorization makes apparent those factors corresponding to all zeros in such a union.

Keywords: generalized exponential polynomials, the Skolem-Mahler-Lech property, factorization

Classification (MSC2000): 30D05; 30D15, 11L99

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