We establish the transition behavior of Jacquet–Whittaker functions on split semi-simple Lie groups. As a consequence, we show that for certain finite volume Riemannian manifolds, the local bound for normalized Laplace eigenfunctions does not hold globally.

中文翻译：

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$$ \ mathrm {GL} _n $$ GL n上的较大的尖峰形式

我们在分裂的半简单Lie群上建立了Jacquet–Whittaker函数的过渡行为。结果，我们表明，对于某些有限体积的黎曼流形，归一化拉普拉斯特征函数的局部界不全局成立。