Zeros of Dirichlet polynomials via a density criterion
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Data
2019-10-01
Autores
Oliveira, Willian D. [UNESP]
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Editor
Elsevier B.V.
Resumo
We obtain a necessary and sufficient condition in order that a semi-plane of the form R(s) > r, r is an element of R, is free of zeros of a given Dirichlet polynomial. The result may be considered a natural generalisation of a well-known criterion for the truth of the Riemann hypothesis due to Baez-Duarte. An analog for the case of Dirichlet polynomials of a result of Burnol which is closely related to Baez-Duarte's one is also established. (C) 2018 Elsevier Inc. All rights reserved.
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Palavras-chave
The Nyman-Beurling criterion, Baez-Duarte's criterion, Dirichlet polynomial, Semi-plane free of zeros, Lubinsky's Dirichlet orthogonal polynomials
Como citar
Journal Of Number Theory. San Diego: Academic Press Inc Elsevier Science, v. 203, p. 80-94, 2019.