Artículo
Carando, D.; Defant, A.; García, D.; Maestre, M.; Sevilla-Peris, P. "The Dirichlet-Bohr radius" (2015) Acta Arithmetica. 171(1):23-37
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Abstract:
Denote by Ω(n) the number of prime divisors of n ∈ ℕ (counted with multiplicities). For x ∈ ℕ define the Dirichlet-Bohr radius L(x) to be the best r > 0 such that for every finite Dirichlet polynomial Σn≤xann-s we have ∑n ≤ x |an| rΩ(n) ≤ supt ∈ ℝ | ∑n ≤ x ann-it|. We prove that the asymptotically correct order of L(x) is (log x)1/4x-1/8. Following Bohr's vision our proof links the estimation of L(x) with classical Bohr radii for holomorphic functions in several variables. Moreover, we suggest a general setting which allows translating various results on Bohr radii in a systematic way into results on Dirichlet-Bohr radii, and vice versa. Copyright © 2007-2014 by IMPAN. All rights reserved.
Registro:
| Documento: | Artículo |
| Título: | The Dirichlet-Bohr radius |
| Autor: | Carando, D.; Defant, A.; García, D.; Maestre, M.; Sevilla-Peris, P. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pab I, Ciudad Universitaria, Buenos Aires, 1428, Argentina IMAS, CONICET, Argentina Institut für Mathematik, Universität Oldenburg, Oldenburg, D26111, Germany Departamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, Burjasot (Valencia), 46100, Spain Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Valencia, Spain |
| Palabras clave: | Bohr radius; Dirichlet series; Holomorphic functions |
| Año: | 2015 |
| Volumen: | 171 |
| Número: | 1 |
| Página de inicio: | 23 |
| Página de fin: | 37 |
| DOI: | http://dx.doi.org/10.4064/aa171-1-3 |
| Título revista: | Acta Arithmetica |
| Título revista abreviado: | Acta Arith. |
| ISSN: | 00651036 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00651036_v171_n1_p23_Carando |
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Citas:
---------- APA ----------
Carando, D., Defant, A., García, D., Maestre, M. & Sevilla-Peris, P. (2015) . The Dirichlet-Bohr radius. Acta Arithmetica, 171(1), 23-37.http://dx.doi.org/10.4064/aa171-1-3
---------- CHICAGO ----------
Carando, D., Defant, A., García, D., Maestre, M., Sevilla-Peris, P. "The Dirichlet-Bohr radius" . Acta Arithmetica 171, no. 1 (2015) : 23-37.http://dx.doi.org/10.4064/aa171-1-3
---------- MLA ----------
Carando, D., Defant, A., García, D., Maestre, M., Sevilla-Peris, P. "The Dirichlet-Bohr radius" . Acta Arithmetica, vol. 171, no. 1, 2015, pp. 23-37.http://dx.doi.org/10.4064/aa171-1-3
---------- VANCOUVER ----------
Carando, D., Defant, A., García, D., Maestre, M., Sevilla-Peris, P. The Dirichlet-Bohr radius. Acta Arith. 2015;171(1):23-37.http://dx.doi.org/10.4064/aa171-1-3
