On the asymptotics of Hecke operators for reductive groups

Tobias Finis; Jasmin Matz

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arXiv · 1905.09078

On the asymptotics of Hecke operators for reductive groups

Tobias Finis·Jasmin Matz

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Abstract

In this paper, we study the asymptotic behavior of the traces of Hecke operators for spherical discrete automorphic representations of fixed level on general split reductive groups over $\mathbb{Q}$. Under a condition on the analytic behavior of intertwining operators, which is known for the classical groups and the exceptional group $G_2$, we obtain the expected asymptotics in terms of the spherical Plancherel measure and an explicit estimate for the remainder.

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Tobias Finis, Jasmin Matz. 2019-05-22. On the asymptotics of Hecke operators for reductive groups. https://arxiv.org/abs/1905.09078

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