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

Valentin Blomer; Félicien Comtat

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arXiv · 2405.10827

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

Valentin Blomer·Félicien Comtat

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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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Valentin Blomer, Félicien Comtat. 2024-05-17. Moments of symmetric square L-functions on GL(3). https://arxiv.org/abs/2405.10827

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