Journal of the Ramanujan Mathematical Society

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A Rankin-Selberg Integral Using the Automorphic Minimal Representation of SO(7)


Affiliations
1 Department of Mathematics, Stanford University, Stanford, CA 94305-2125, United States
2 Department of Mathematics, Boston College, Chestnut Hill, MA 02467-3806, United States
3 School of Mathematical Sciences, Sadder Faculty of Exact Sciences, Tel Aviv University, Ramat-Aviv, 69978, Israel
     

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We show that a certain residue of a metaplectic Eisenstein series on SO7 affords the automorphic minimal representation, whose local theory was described by Torasso, Roskies and Sabourin. As an application, we give a Rankin-Selberg construction of the Langlands L-function for the third fundamental representation of the L-group Sp(6,C), which is an Euler product of degree 14 attached to a generic cusp form on SO7.
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  • A Rankin-Selberg Integral Using the Automorphic Minimal Representation of SO(7)

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Authors

Daniel Bump
Department of Mathematics, Stanford University, Stanford, CA 94305-2125, United States
Solomon Friedberg
Department of Mathematics, Boston College, Chestnut Hill, MA 02467-3806, United States
David Ginzburg
School of Mathematical Sciences, Sadder Faculty of Exact Sciences, Tel Aviv University, Ramat-Aviv, 69978, Israel

Abstract


We show that a certain residue of a metaplectic Eisenstein series on SO7 affords the automorphic minimal representation, whose local theory was described by Torasso, Roskies and Sabourin. As an application, we give a Rankin-Selberg construction of the Langlands L-function for the third fundamental representation of the L-group Sp(6,C), which is an Euler product of degree 14 attached to a generic cusp form on SO7.