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A Cuspidality Criterion for the Functorial Product on GL(2) × GL(3) with a Cohomological Application

Ramakrishnan, Dinakar and Wang, Song (2004) A Cuspidality Criterion for the Functorial Product on GL(2) × GL(3) with a Cohomological Application. International Mathematics Research Notices, 2004 (27). pp. 1355-1394. ISSN 1073-7928. doi:10.1155/S1073792804132856.

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For all cusp forms π on GL(3) and π′ on GL(2) over a number field F, H. Kim and F. Shahidi have functorially associated an automorphic form Formula on GL(6) such that L(s, Π) agrees with the Rankin-Selberg L-function of the pair (π, π′). First we establish a criterion as to when Π is cuspidal. Then we apply it to construct non-self-dual, nonmonomial cuspidal cohomology classes for suitable congruence subgroups of SL(3, ℤ). We also analyze the Galois image of certain related ℓ-adic representations.

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Wang, Song0000-0003-3116-5038
Additional Information:© 2004 Hindawi Publishing Corporation. Received 17 September 2003. Revision received 14 January 2004. Accepted March 22, 2004. Communicated by Freydoon Shahidi. The first author would like to thank Avner Ash for his question and for making comments on an earlier version of this paper, Freydoon Shahidi for his interest, Mahdi Asgari for initially tweaking his curiosity (at Park City, UT) about the problem of establishing a precise cuspidality criterion for the Kim-Shahidi product, David Rohrlich for his comments on Hecke characters, and the National Science Foundation for financial support through Grant DMS-0100372. The second author would like to thank James Cogdell and Henry Kim for their interest in his lecture on this work at the Fields Institute Workshop on Automorphic L-functions in May 2003.Both authors thank the referee for a careful reading of the paper.
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Issue or Number:27
Record Number:CaltechAUTHORS:20111019-072552735
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Official Citation: Dinakar Ramakrishnan and Song Wang A cuspidality criterion for the functorial product on GL(2) × GL(3) with a cohomological application Int Math Res Notices (2004) Vol. 2004 1355-1394 doi:10.1155/S1073792804132856
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27291
Deposited By: Ruth Sustaita
Deposited On:19 Oct 2011 14:52
Last Modified:09 Nov 2021 16:47

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