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- W2949485798 abstract "Let E/F be a quadratic extension of number fields. For a cuspidal representation $pi$ of SL(2,A_E), we study the non-vanishing of the period integral on SL(2,F)SL(2,A_F). We characterise the non-vanishing of the period integral of $pi$ in terms of $pi$ being generic with respect to characters of EA_E which are trivial on A_F. We show that the period integral in general is not a product of local invariant functionals, and find a necessary and sufficient condition when it is. We exhibit cuspidal representations of SL(2,A_E) whose period integral vanishes identically while each local constituent admits an SL(2)-invariant linear functional. Finally, we construct an automorphic representation $pi$ on SL(2,A_E) which is abstractly SL(2,A_F) distinguished but none of the elements in the global L-packet determined by $pi$ is distinguished by SL(2,A_F)." @default.
- W2949485798 created "2019-06-27" @default.
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- W2949485798 date "2004-12-10" @default.
- W2949485798 modified "2023-09-27" @default.
- W2949485798 title "On the SL(2) period integral" @default.
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