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

Published online by Cambridge University Press:  20 November 2018

Aaron Pollack  and
Shrenik Shah
Aaron Pollack
Affiliation:
School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA, e-mail : aaronjp@math.ias.edu
Shrenik Shah
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10027, USA, e-mail : snshah@math.columbia.edu
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Abstract

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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.

Keywords

11F6611F55automorphic formL-functionRankin–Selbergmethodunitary groupexterior squareLanglands program
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 4 , 01 December 2018 , pp. 822 - 835
Copyright
Copyright © Canadian Mathematical Society 2018

References

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