Beyond endoscopy for the Rankin-Selberg L-function

2010/03/01 by Herman, P. Edward
#11F66 #11F72 #11M06 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1003.0462

Abstract

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.

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