Asymptotics for cuspidal representations by functoriality from GL(2)

Huixue Lao, Mark McKee, Yangbo Ye

Let $\pi$ be a unitary automorphic cuspidal representation of $G{L}_2({\mathbb{Q}}_{\mathbb{A}})$ with Fourier coefficients ${\lambda }_{\pi }(n)$. Asymptotic expansions of certain sums of ${\lambda }_{\pi }(n)$ are…