#### Abstract

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

**, and find out which**

*E*_{6}*-functions they represent. The heuristics also predict the existence of a fourth integral.*

**L**#### Recommended Citation

Ginzburg, David and Hundley, Joseph. "A New Tower of Rankin-Selberg Integrals." (Jan 2006).

## Comments

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in

Electronic Research Announcements of the American Mathematical Societyfollowing peer review. The definitive publisher-authenticated version inElectronic Research Announcements of the American Mathematical Societyvol. 12 (2006), 56-62. is available online at: http://www.ams.org/era/2006-12-08/S1079-6762-06-00160-0/S1079-6762-06-00160-0.pdf and at http://www.aimsciences.org/journals/pdfs.jsp?paperID=2292&mode=full. © 2006 American Mathematical Society