Abstract.
This is the second of four papers that study algebraic
and analytic structures associated with the Lerch zeta function.
The Lerch zeta function
(s,a,c):= n=0 e 2ina (n+c) s
was introduced by Lipschitz in 1857,
and is named after Lerch, who showed in 1887 that it satisfied
a functional equation. Here we analytically continue
(s,a,c) as a function of three complex variables.
We show that it is well-defined as a multivalued function
on the manifold
:=(s,a,c)()(), and that
this analytic continuation becomes single-valued on the maximal abelian cover of 
.
We compute the monodromy functions describing the multivalued
nature of this function on 
, and determine various of
its properties.
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