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Recovering Cusp Forms on GL(2) from Symmetric Cubes

Ramakrishnan, Dinakar (2015) Recovering Cusp Forms on GL(2) from Symmetric Cubes. In: SCHOLAR—a Scientific Celebration Highlighting Open Lines of Arithmetic Research. Contemporary Mathematics. No.655. American Mathematical Society , Providence, RI. ISBN 978-1-4704-1457-3.

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Suppose π, π′ are cusp forms on GL(2), not of solvable polyhedral type, such that they have the same symmetric cubes. Then we show that either π, π′ are twist equivalent, or else a certain degree 36 L-function associated to the pair has a pole at s=1. If we further assume that the symmetric fifth power of π is automorphic, then in the latter case, π is icosahedral in a suitable sense, agreeing with the usual notion when there is an associated Galois representation.

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Additional Information:© 2015 American Mathematical Society. This article is dedicated to Ram Murty, a friend whose works I have long read with interest.
Series Name:Contemporary Mathematics
Issue or Number:655
Record Number:CaltechAUTHORS:20160211-083113741
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64408
Deposited By: Tony Diaz
Deposited On:19 Feb 2016 00:57
Last Modified:03 Oct 2019 09:37

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