On the Rankin–Selberg convolution of degree 2 functions from the extended Selberg class
Volume 118 / 2019
Banach Center Publications 118 (2019), 25-35
MSC: Primary 11M41, 11F30.
DOI: 10.4064/bc118-2
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 $F\otimes \overline {F}(s)$ has holomorphic continuation to the half-plane $\sigma \gt \theta $ apart from a simple pole at $s=1$, where $1/2 \lt \theta \lt 1$ depends on the above mentioned bounds.
