| This paper extends a result of Woodson on seesaw identities over adelic groups, inspired by the ideas of Kudla, Bump, and Goldfeld. The first chapter is written in the classical setting and reproves the result by Zagier that allows one to apply the Rankin-Selberg method to functions that are not of rapid decay. The second chapter uses Zagier's idea in the adelic setting, along with the parallel result by Bump and Beineke to construct a seesaw identity in the ambient group GL(8, A ). The identity relates the integral of a product of two Eisenstein series and a GL(2, A ) cusp form with the Mellin transform of that cusp form. In the third chapter, a similar calculation is done with the GL(2, A ) cusp form replaced with a GL(2, A ) Eisenstein series and a similar identity is proven. |
