On the Moments of Exponential Sums over r-Free Polynomials
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908421699141632 |
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| author | Doyle, Ben |
| author_facet | Doyle, Ben |
| contents | Let $\mathbb{F}_q[t]$ denote the ring of polynomials over the finite field $\mathbb{F}_q$. Building off of techniques of Balog and Ruzsa and of Keil in the integer setting, we determine the precise order of magnitude of $k$th moments of exponential sums over $r$-free polynomials in $\mathbb{F}_q[t]$ for all $k>0$. In the supercritical case $k>1+1/r$, we acquire an asymptotic formula using a function field analogue of the Hardy-Littlewood circle method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20581 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Moments of Exponential Sums over r-Free Polynomials Doyle, Ben Number Theory 11T55 (Primary) 11L07, 11P55 (Secondary) Let $\mathbb{F}_q[t]$ denote the ring of polynomials over the finite field $\mathbb{F}_q$. Building off of techniques of Balog and Ruzsa and of Keil in the integer setting, we determine the precise order of magnitude of $k$th moments of exponential sums over $r$-free polynomials in $\mathbb{F}_q[t]$ for all $k>0$. In the supercritical case $k>1+1/r$, we acquire an asymptotic formula using a function field analogue of the Hardy-Littlewood circle method. |
| title | On the Moments of Exponential Sums over r-Free Polynomials |
| topic | Number Theory 11T55 (Primary) 11L07, 11P55 (Secondary) |
| url | https://arxiv.org/abs/2506.20581 |