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arXiv · 1202.5703

Construction of an Ordinary Dirichlet Series with Convergence beyond the Bohr Strip

Brian N. Maurizi
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Abstract

An ordinary Dirichlet series has three abscissae of interest, describing the maximal regions where the Dirichlet series converges, converges uniformly, and con- verges absolutely. The paper of Hille and Bohnenblust in 1931, regarding the region on which a Dirichlet series can converge uniformly but not absolutely, has prompted much investigation into this region, the "Bohr strip". However, a related natural question has apparently gone unanswered: For a Dirichlet series with non-trivial Bohr strip, how far beyond the Bohr strip might the series converge? We investigate this question by explicit construction, creating Dirichlet series which converge beyond their Bohr strip.

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Brian N. Maurizi. 2012-02-25. Construction of an Ordinary Dirichlet Series with Convergence beyond the Bohr Strip. https://arxiv.org/abs/1202.5703

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