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.

中文翻译：

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关于还原群的Hecke算子的渐近性

在本文中，我们研究了\（\ mathbb {Q} \）上一般拆分归约组上固定水平的球形离散自同构表示的Hecke算子迹线的渐近行为。在经典算子和例外算子\（G_2 \）相互交织的分析行为的条件下，我们根据球面Plancherel测度获得了期望的渐近性，并对其余部分进行了显式估计。