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## 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.

#### Authors

• Jerzy KaczorowskiFaculty of Mathematics and Computer Science
Umultowska 87
61-614 Poznań, Poland
and
Institute of Mathematics of the Polish Academy of Sciences
00-656 Warsaw, Poland
e-mail
• Alberto PerelliDipartimento di Matematica
Università di Genova
via Dodecaneso 35
16146 Genova, Italy
e-mail

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