On the Rankin–Selberg convolution of degree 2 functions from the extended Selberg class

Volume 118 / 2019

Jerzy Kaczorowski, Alberto Perelli Banach Center Publications 118 (2019), 25-35 MSC: Primary 11M41, 11F30. DOI: 10.4064/bc118-2


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.


  • Jerzy KaczorowskiFaculty of Mathematics and Computer Science
    Adam Mickiewicz University
    Umultowska 87
    61-614 Poznań, Poland
    Institute of Mathematics of the Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warsaw, Poland
  • Alberto PerelliDipartimento di Matematica
    Università di Genova
    via Dodecaneso 35
    16146 Genova, Italy

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