Geodesic
The Bohr inequality for ordinary Dirichlet series
R. Balasubramanian 1   ; B. Calado 2   ; H. Queffélec 3
1 The Institute of Mathematical Sciences Chennai 600 113, India
2 Laboratoire de Mathématiques Centre d'Orsay Université Paris-Sud XI Bâtiment 425 91405 Orsay, France
3 UFR de Mathématiques Université de Lille 1 59655 Villeneuve d'Ascq Cedex, France
Studia Mathematica, Tome 175 (2006) no. 3, pp. 285-304 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $f(s) = \sum_{n=1}^{\infty}a_nn^{-s}$ with $\| f \|_{\infty} := \sup_{\Re s > 0} |f(s)| \infty$, then $\sum_{n=1}^{\infty}|a_n|n^{-2} \leq \| f \|_{\infty}$ and even slightly better, and $\sum_{n=1}^{\infty}|a_n|n^{-1/2} \leq C\| f \|_{\infty}$, $C$ being an absolute constant.
DOI : 10.4064/sm175-3-7
Keywords: extend setting dirichlet series previous results bohr taylor series variable themselves generalized paulsen popescu nbsp singh extended several variables aizenberg boas khavinson particular sum infty s infty sup infty sum infty leq infty even slightly better sum infty leq infty being absolute constant

R. Balasubramanian  1   ; B. Calado  2   ; H. Queffélec  3

1 The Institute of Mathematical Sciences Chennai 600 113, India
2 Laboratoire de Mathématiques Centre d'Orsay Université Paris-Sud XI Bâtiment 425 91405 Orsay, France
3 UFR de Mathématiques Université de Lille 1 59655 Villeneuve d'Ascq Cedex, France 
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R. Balasubramanian; B. Calado; H. Queffélec. The Bohr inequality for ordinary Dirichlet series. Studia Mathematica, Tome 175 (2006) no. 3, pp. 285-304. doi: 10.4064/sm175-3-7

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