  We study numerical integration for a weighted Korobov space of analytic
periodic functions for which the Fourier coefficients decay exponentially fast.
In particular, we are interested in how the error depends on the dimension $d$.
Many recent papers deal with this problem or similar problems and provide
matching necessary and sufficient conditions for various notions of
tractability. In most cases even simple algorithms are known which allow to
achieve these notions of tractability. However, there is a gap in the
literature: while for the notion of exponential-weak tractability one knows
matching necessary and sufficient conditions, so far no explicit algorithm has
been known which yields the desired result.
  In this paper we close this gap and prove that Korobov lattice rules are
suitable algorithms in order to achieve exponential-weak tractability for
integration in weighted Korobov spaces of analytic periodic functions.
