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The Quarterly Journal of Mathematics Advance Access originally published online on November 25, 2007
The Quarterly Journal of Mathematics 2008 59(2):189-205; doi:10.1093/qmath/ham028
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© 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

THE ARITHMETIC BOHR RADIUS

Andreas Defant{dagger}

Institute of Mathematics, Carl von Ossietzky University, D-26111 Oldenburg, Germany

Manuel Maestre {ddagger}

University of Valencia, Doctor Moliner 50, 46100 Burjasot, Valencia, Spain

Christopher Prengel §

Institute of Mathematics, Carl von Ossietzky University, D-26111 Oldenburg, Germany

{dagger} Corresponding author. E-mail: defant{at}mathematik.uni-oldenburg.de

Received 8 December 2006;
  Abstract

We study the arithmetic Bohr radius of Reinhardt domains in Cn which was successfully used in our study of monomial expansions for holomorphic functions in infinite dimensions. We show that this new Bohr radius is different from the radii invented by Boas and Khavinson and Aizenberg. It gives an explicit formula for the n-dimensional hypercone (which means n-dimensional variants of classical results of Bohr and Bombieri), and moreover asymptotically corrects upper and lower estimates for various types of convex and non-convex Reinhardt domains.

{ddagger} E-mail: manuel.maestre{at}uv.es

§ E-mail: c.prengel{at}uni-oldenburg.de


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