Let $F(s)$ be a function of degree $2$ from the extended Selberg class. Assuming certain bounds for the shifted convolution sums associated with $F(s)$, we prove that the Rankin-Selberg convolution $Fhskip-.07cmotimes hskip-.07cmoverline{F}(s)$ has holomorphic continuation to the half-plane $si> heta$ apart from a simple pole at $s=1$, where $1/2< heta<1$ depends on the above mentioned bounds.
On the Rankin-Selberg convolution of degree $2$ functions from the extended Selberg class
PERELLI, A.
2019-01-01
Abstract
Let $F(s)$ be a function of degree $2$ from the extended Selberg class. Assuming certain bounds for the shifted convolution sums associated with $F(s)$, we prove that the Rankin-Selberg convolution $Fhskip-.07cmotimes hskip-.07cmoverline{F}(s)$ has holomorphic continuation to the half-plane $si> heta$ apart from a simple pole at $s=1$, where $1/2< heta<1$ depends on the above mentioned bounds.
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