We recall the notion of a tower of Rankin-Selberg integrals, and two known towers, making observations of how the integrals within a tower may be related to one another via formal manipulations, and offering a heuristic for how the L-functions should be related to one another when the integrals are related in this way. We then describe three new integrals in a tower on the group E6, and find out which L-functions they represent. The heuristics also predict the existence of a fourth integral.
Ginzburg, David and Hundley, Joseph. "A New Tower of Rankin-Selberg Integrals." (Jan 2006).