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Second order average estimates on local data of cusp forms

Farrell Brumley
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Abstract

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 at present satisfied for n less than or equal to 4. As an application, we show that Rankin-Selberg L-functions on GL(m) x GL(n), when m and n are less than or equal to 4, satisfy the standard convexity bound.

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Farrell Brumley. 2005-10-05. Second order average estimates on local data of cusp forms. https://arxiv.org/abs/math/0510089

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