Second order average estimates on local data of cusp forms

Farrell Brumley (1)

1 IECN - Institut Élie Cartan de Nancy

We specify sufficient conditions for the square modulus of the local parameters of a family of GL(n) cusp forms to be bounded on average. These conditions are global in nature and are satisfied for n less than or equal to 4. As an application, we show that Rankin-Selberg L-functions on GL(n_1) ×GL(n_2) , for n_i less than or equal to 4, satisfy the standard covexity bound.

Domaines: Théorie des nombres [math.NT]

Farrell Brumley. Second order average estimates on local data of cusp forms. Archiv der Mathematik, 2006, pp.19-32. ⟨10.1007/s00013-005-1632-3⟩. ⟨hal-00142725⟩