An exercise concerning the selfdual cusp forms on GL(3)

Dinakar Ramakrishnan ()

Indian Journal of Pure and Applied Mathematics, 2014, vol. 45, issue 5, 777-785

Abstract: Abstract Using L-functions and various known results, we provide a proof of the following Let F be a number field and II a cuspidal automorphic form on GL(3)/F which is selfdual. Then, up to replacing II by a quadratic twist, it can be realized as the adjoint of a cusp form π on GL(2)/F, with π unramified at any prime where II is. We also investigate the properties of π when II is regular and algebraic.

Keywords: Selfdual representations; automorphic forms; symmetric square; adjoint (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s13226-014-0088-1

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