On the growth of cuspidal cohomology of ${\mathrm{GL}}_4$

Abstract

In this article, we establish an asymptotic estimate on the number of cuspidal automorphic representations of ${\mathrm{GL}}_4({\mathbb{A}}_{\mathbb{Q}})$ which contribute to the cuspidal cohomology of ${\mathrm{GL}}_4$ and are obtained from symmetric cube transfer of automorphic representations of ${\mathrm{GL}}_2({\mathbb{A}}_{\mathbb{Q}})$ of a given weight and with varying level structure. This generalises the recent work of C. Ambi [2020] about the similar problem for ${\mathrm{GL}}_3$.

11 Pages, minor revisions made before the final acceptance in the journal

References in corpus (1)

• Endoscopy and the cohomology of GL(n)

Cited by in corpus (2)

• Two properties of symmetric cube transfers of modular forms
• Automorphic tensor products and cuspidal cohomology of the ${\mathrm{GL}}_4$