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
Full text of the article: