Moments of symmetric square L-functions on GL(3)

2024/05/17 by Blomer, Valentin, Comtat, Félicien
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2405.10827

Abstract

We give an asymptotic formula with power saving error term for the twisted first moment of symmetric square L-functions on GL(3) in the level aspect. As applications, we obtain non-vanishing results as well as lower bounds of the expected order of magnitude for all even moments, supporting the random matrix model for a unitary ensemble. Besides the GL(3) Kuznetsov formula, the ingredients include detailed local computations at ramified places, including root numbers and orthonormalization of oldforms and Eisenstein series.

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