| A Dirichlet series is an infinite series of type a(1) + a (2)2^{-s} + a(3) 3^{-s} + . . . where s is a complex variable. Examples include the Riemann zeta function. A multiple Dirichlet series (MDS) is a Dirichlet series in a variable s whose coefficients a(1), a(2), . . . are Dirichlet series in another variable, etc. MDS may be viewed as Dirichlet series in several complex variables. We survey what is known about MDS and explain connections of MDS with the theory of classical Lie groups. |