The second moment of -functions at special points
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For a fixed SL(3, ℤ) Maass form φ, we consider the family of L-functions L(φ × uj, s) where uj runs over the family of Hecke-Maass cusp forms on SL(2, ℤ). We obtain an estimate for the second moment of this family of L-functions at the special points 1/2 + itj consistent with the Lindelöf Hypothesis. We also obtain a similar upper bound on the sixth moment of the family of Hecke-Maass cusp forms at these special points; this is apparently the first occurrence of a Lindelöf-consistent estimate for a sixth power moment of a family of GL(2) L-functions. © 2012 Springer-Verlag Berlin Heidelberg.
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