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

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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.

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Authors and Affiliations

  1. 253-37 Caltech, Pasadena, CA, 91125, USA

    Dinakar Ramakrishnan

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  1. Dinakar Ramakrishnan
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Correspondence to Dinakar Ramakrishnan.

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Ramakrishnan, D. An exercise concerning the selfdual cusp forms on GL(3). Indian J Pure Appl Math 45, 777–785 (2014). https://doi.org/10.1007/s13226-014-0088-1

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  • DOI: https://doi.org/10.1007/s13226-014-0088-1

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