Multivariate Rankin–Selberg Integrals on GL4 and GU(2, 2)

Pollack, Aaron ; Shah, Shrenik

Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 822-835

Résumé

Inspired by a construction by Bump, Friedberg, and Ginzburg of a two-variable integral representation on $\text{GS}{{\text{p}}_{4}}$ for the product of the standard and spin $L$ -functions, we give two similar multivariate integral representations. The first is a three-variable Rankin-Selberg integral for cusp forms on $\text{PG}{{\text{L}}_{4}}$ representing the product of the $L$ -functions attached to the three fundamental representations of the Langlands $L$ -group $\text{S}{{\text{L}}_{\text{4}}}\left( \text{C} \right)$ . The second integral, which is closely related, is a two-variable Rankin-Selberg integral for cusp forms on $\text{PGU}\left( 2,\,2 \right)$ representing the product of the degree $8$ standard $L$ -function and the degree $6$ exterior square $L$ -function.

Détail

DOI : 10.4153/CMB-2018-003-2

Mots-clés : 11F66, 11F55, automorphic form, L-function, Rankin–Selbergmethod, unitary group, exterior square, Langlands program