
## 4. Applications

1. #### Problem 4.1.

[E. Lapid] Are there instances of Rankin-Selberg methods for higher covers?
• #### Problem 4.2.

[E. Lapid] What global covering groups have arithmetic applications?
• #### Problem 4.3.

[W. Gan] Are there applications of the invariant trace formula for $\widetilde{G}_{F}$?
• #### Problem 4.4.

[P. Trapa] Interpret formal degrees of representations of $\widetilde{G}_{F}$ on level of Hecke algebra. (à la Opdam, Reeder, et al)
• #### Problem 4.5.

Are there global applications of the trace formula, automorphic forms, Whittaker models, the Langlands-Shahidi method for $\widetilde{G}$ ?

– Classify automorphic representations of covers of split tori.
• #### Problem 4.6.

Study the residual spectrum for $\widetilde{GL}(n)$.

– Can the lifting of Levi subgroups be done over $p$-adic? If so, is it one of the Brylinski-Deligne extensions?

– Describe covers of $GL(n)$ not arising from Kazhdan-Petterson.

Cite this as: AimPL: Automorphic forms on covering groups, available at http://aimpl.org/autoformcovergp.