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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.04461 |
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Table of Contents:
- Let $λ$ denote the Liouville function for function fields. We prove that for a fixed $q$, given $h \ll \sqrt{N}$ and $h(N) \to \infty$ arbitrarily slowly as $N \to \infty$, then \begin{equation*} \frac{1}{q^N}\sum_{G_0 \in \mathcal{M}_N}|\sum_{G \in \mathcal{I}_{h}(G_0)}λ(G)|^2 \ll_q \frac{N^5}{h^2}q^{h}. \end{equation*} The proof follows a similar method of an analogous case in the integer setting developed by Chinis, adapting methods originally developed by Matomäki and Radziwiłł.