A nonabelian trace formula

Abstract

Let $E/F$ be an extension of number fields with $\mathrm{Gal}(E/F)$ simple and nonabelian. In [G] the first named author suggested an approach to nonsolvable base change and descent of automorphic representations of ${\mathrm{GL}}_2$ along such an extension. Motivated by this we prove a trace formula whose spectral side is a weighted sum over cuspidal automorphic representations of ${\mathrm{GL}}_2({\mathbb{A}}_E)$ that are isomorphic to their $\mathrm{Gal}(E/F)$-conjugates.

Comments are welcome

References in corpus (1)

• The subconvexity problem for $\GL_{2}$

Cited by in corpus (1)

• Invariant four-variable automorphic kernel functions