Given a pair of distinct unitary cuspidal automorphic representations for GL(n) over a number field, let S denote the set of finite places at which the automorphic representations are unramified and their associated Hecke eigenvalues differ. In this paper, we demonstrate how conjectures on the automorphy and possible cuspidality of adjoint lifts and Rankin–Selberg products imply lower bounds on the size of S. We also obtain further results for GL(3).

中文翻译：

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GL(n) 强多重性一的猜想改进

给定一对不同的酉尖自守表示 GL(n) 在一个数字域上，让小号表示自守表示未分枝且其关联的 Hecke 特征值不同的有限位置集合。在本文中，我们展示了关于伴随升降机和 Rankin-Selberg 乘积的自同形和可能尖峰性的猜想如何暗示小号. 我们还获得了进一步的结果总帐(3).