Maass forms on GL(3) and GL(4)

Abstract

We describe a practical method for finding an L-function without first finding the associated underlying object. The procedure involves using the Euler product and the approximate functional equation in a new way. No use is made of the functional equation of twists of the L-function. The method is used to find a large number of Maass forms on SL(3,Z) and to give the first examples of Maass forms of higher level on GL(3), and on GL(4) and Sp(4).