The Second Moment of Gl(3)×gl(2) L-functions at Special Points
نویسنده
چکیده
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.
منابع مشابه
The Second Moment of Gl(3)×gl(2) L-functions, Integrated
We consider the family of Rankin-Selberg convolution L-functions of a fixed SL(3,Z) Maass form with the family of Hecke-Maass cusp forms on SL(2,Z). We estimate the second moment of this family of L-functions with a “long” integration in t-aspect. These L-functions are distinguished by their high degree (12) and large conductors (of size T ).
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