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

We describe a practical method for finding an L-function without first finding an associated underlying object. The procedure involves using the Euler product, the Ramanujan bound, 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 ${\mathrm SL}(3,\mathbb Z)$ and to...