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Jun 4, 2014 at 22:56 comment added Aurel Thanks for the correction. I am not an expert at all, so I just copied the statement.
Jun 4, 2014 at 22:21 comment added Lucia One really needs only the holomorphy of these symmetric powers in Re$(s)>1$ (rather than absolute convergence -- of course, once Ramanujan follows then holomorphy becomes absolute convergence). The letter from Serre to Deshouillers which is reproduced in the Blomer-Brumley article gives a sketch argument, which Serre attributes to Langlands and Deligne. See also page 666 of this article by Sarnak: web.math.princeton.edu/sarnak/FieldNotesCurrent.pdf
Jun 4, 2014 at 22:18 history answered Aurel CC BY-SA 3.0