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 we have . We prove that the asymptotically correct order of L(x) is . 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-1-3,
author = {Daniel Carando and Andreas Defant and Domingo A. Garc\'\i\ and Manuel Maestre and Pablo Sevilla-Peris},
title = {The Dirichlet-Bohr radius},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {23-37},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-1-3}
}
Daniel Carando; Andreas Defant; Domingo A. Garcí; Manuel Maestre; Pablo Sevilla-Peris. The Dirichlet-Bohr radius. Acta Arithmetica, Tome 168 (2015) pp. 23-37. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-1-3/