Abstract We estimate the growth of cuspidal cohomology of G L 2 ( A Q ) . Quantitatively, we provide bounds on the total number of normalised eigenforms of Hecke operators which are obtained by automorphic induction from Hecke characters of imaginary quadratic fields grows as level structure varies. We further investigate how much of cuspidal cohomology of G L 3 ( A Q ) is obtained by symmetric square transfer from G L 2 ( A Q ) when the level structure corresponds to power of an odd prime.

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关于GL(2)和GL(3)的尖瓣上同调的增长

摘要 我们估计了GL 2 (AQ) 的尖瓣上同调的增长。从数量上讲，我们提供了 Hecke 算子归一化特征形式的总数的界限，这些特征形式是通过自守归纳从虚二次域的 Hecke 特征中获得的，随着层次结构的变化而增长。我们进一步研究了当能级结构对应于奇素数的幂时，GL 3 ( AQ ) 的尖顶上同调有多少是通过从 GL 2 ( AQ ) 的对称平方转移获得的。