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Note on the Shapiro polynomials

1970; American Mathematical Society; Volume: 25; Issue: 1 Linguagem: Inglês

10.1090/s0002-9939-1970-0260955-6

ISSN

1088-6826

Autores

John Brillhart, L. Carlitz,

Tópico(s)

Advanced Mathematical Identities

Resumo

where n > 0 and Po(x) = Qo(x) = 1. (See [4] also. Note in this reference that Po(x) =Qo(x) =x.) These polynomials have been used by Kahane and Salem in their book [1 ] to prove several theorems about trigonometric series. Rider [2] used a generalization of these polynomials to complete the solution of a problem partially solved in [4]. In a more recent paper Rider [3] employed the polynomials to exhibit certain subalgebras of the group algebra of the unit circle. In particular, in this paper Rider obtained a special case of Theorem 4 below. The first few polynomials are

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