On a cubic lifting
The cubic lifting in the title is a correspondence between automorphic representations of \(G = \text{SL}_2\) over a number field containing the cubic roots of unity and automorphic representations of the three-fold cover \(\widetilde G\) of \(G\). This lifting is defined and studied in \textit{D. Ginzburg, S. Rallis, D. Soudry} [Am. J. Math. 119, 251-335 (1997; Zbl 0877.11031)]. The present paper completes [loc. cit.] by showing that any irreducible cuspidal representation of \(\widetilde G\) has a cubic lift to \(G\). This is done by a now well-known method, namely by establishing and exploiting a relative trace formula.
scientific article; zbMATH DE number 1389705
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