the lerch zeta function is a three variable zeta function, with variables $(s, a, c)$, which generalizes the riemann zeta function and has a functional equation, but no euler product. we discuss its properties. it is an eigenfunction of a linear partial differential equation in the variables $(a, c)$ with eigenvalue $-s$, and it is also preserved under a a commuting family of two-variable hecke-operators $t_m$ with eigenvalue $m^{-s}$. we give a characterization of it in terms of being a simultaneous eigenfunction of these hecke operators. we then give an automorphic interpretation of the lerch zeta function in terms of eisenstein series taking values on the heisenberg nilmanifold, a quotient of the real heisenberg group modulo its integer subgroup. part of this work is joint with w.-c. winnie li.