Square-root cancellation for sums of coefficients of $\operatorname{GL}(m)$-automorphic forms over values of random polynomials

Dimitrios Chatzakos; Efthymios Sofos

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arXiv · 2606.15900

Square-root cancellation for sums of coefficients of $\operatorname{GL}(m)$-automorphic forms over values of random polynomials

Dimitrios Chatzakos·Efthymios Sofos

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Abstract

For arbitrary $m\geq 2$ and $d\geq 1$, we establish square-root cancellation for sums of Fourier coefficients of $\mathrm{GL}(m)$-automorphic forms averaged over values of random degree-$d$ polynomials.

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Dimitrios Chatzakos, Efthymios Sofos. 2026-06-14. Square-root cancellation for sums of coefficients of $\operatorname{GL}(m)$-automorphic forms over values of random polynomials. https://arxiv.org/abs/2606.15900

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