Abstract. We extend to the setting of Dirichlet series previous results of H. Bohr for Taylor series in one variable, themselves generalized by V. I. Paulsen, G. Popescu and D. Singh or extended to several variables by L. Aizenberg, R. P. Boas and D. Khavinson. We show in particular that, if f (s) = ∞ n=1 a n n −s with f ∞ := sup ℜs>0 |f (s)| < ∞, then ∞ n=1 |a n |n −2 ≤ f ∞ and even slightly better, and ∞ n=1 |a n |n −1/2 ≤ C f ∞ , C being an absolute constant.

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