Addendum and corrigendum to the paper “Nonlinear twists and moments of $L$-functions” (Acta Arith. 214 (2024), 153–171)

We correct and refine a conjecture from [Acta Arith. 214 (2024), 153–171] on the analytic behaviour of the self-dual twist associated with the functions $F(s)$ in the extended Selberg class. The corrected version relates the order of the poles to those of the Rankin–Selberg convolution $F \times \overline {F}(s)$ and to the structural invariants $d_F(\ell )$.

Published in Open Access (under CC-BY license).