  We try to understand the poles of L-functions via taking a limit in a trace
formula. This technique avoids endoscopic and Kim-Shahidi methods. In
particular, we investigate the poles of the Rankin-Selberg L-function. Using
analytic number theory techniques to take this limit, we essentially get a new
proof of the analyticity of the Rankin-Selberg L-function at $s=1.$ Along the
way we discover the convolution operation for Bessel transforms.
