  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.
