M\"{o}bius cancellation on polynomial sequences and the quadratic Bateman-Horn conjecture over function fields
2020
We establish cancellation in short sums of certain special trace functions over $\mathbb{F}_q[u]$ below the P\'{o}lya-Vinogradov range, with savings approaching square-root cancellation as $q$ grows. This is used to resolve the $\mathbb{F}_q[u]$-analog of Chowla's conjecture on cancellation in M\"{o}bius sums over polynomial sequences, and of the Bateman-Horn conjecture in degree $2$, for some values of $q$. A final application is to sums of trace functions over primes in $\mathbb{F}_q[u]$.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
37
References
3
Citations
NaN
KQI