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

Phuksuwan, Ouamporn and Laohakosol, Vichian (2011) A factorization theorem for generalized exponential polynomyals with infinitely many integer zeros. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 27 (2). pp. 211-221. ISSN 0866-0174

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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.

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