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 $F\hskip-.07cm\otimes \hskip-.07cm\overline{F}(s)$ has holomorphic continuation to the half-plane $\si>\theta$ apart from a simple pole at $s=1$, where $1/2<\theta<1$ depends on the above mentioned bounds.

### On the Rankin-Selberg convolution of degree $2$ functions from the extended Selberg class

#### 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 $F\hskip-.07cm\otimes \hskip-.07cm\overline{F}(s)$ has holomorphic continuation to the half-plane $\si>\theta$ apart from a simple pole at $s=1$, where $1/2<\theta<1$ depends on the above mentioned bounds.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/934192
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