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arXiv · 2605.20707

Limiting Distribution and Rate of Convergence for GL(3) Fourier Coefficients

Zongqi Yu
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Abstract

In a work of Heath-Brown, it is proved that in the Pilz divisor problem, the normalized error term $\Delta_3(x)$ has a distribution function. In this paper, we prove an analogue of this result in the setting of GL(3). For a given self-dual GL(3) Hecke--Maass cusp form $f$ with normalized Fourier coefficients $A_f(n,m)$, let $\Delta_f(x)=\sum_{n\leqslant x}A_f(n,1)$. We show that the function $x^{-1/3}\Delta_f(x)$ has a distribution function and we obtain a quantitative rate of convergence for the limiting distribution.

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Zongqi Yu. 2026-05-20. Limiting Distribution and Rate of Convergence for GL(3) Fourier Coefficients. https://arxiv.org/abs/2605.20707

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