Beyond endoscopy for the Rankin-Selberg L-function

Details Beyond endoscopy for the Rankin-Selberg L-function Beyond endoscopy for the Rankin-Selberg L-function

2010-03-01

arxiv.org/abs/1003.0462v2

Mathematics

Number Theory

27 pages; accepted to Journal of Number Theory

Scientific paper

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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