论文标题
在多项式序列和功能场上的二次贝特曼猜想上取消Möbius
Möbius cancellation on polynomial sequences and the quadratic Bateman-Horn conjecture over function fields
论文作者
论文摘要
我们以$ \ mathbb {f} _q [u] $低于Pólya-Vinogradov范围的$ \ mathbb {f} _q [u] $的简短款项建立取消，而储蓄接近Square-ot-q $ q $的增长。这用于解决$ \ Mathbb {f} _q [u] $ - 乔拉拉（Chowla）对多项式序列的取消的猜想的类似物，以多项式序列和bateman-horn的猜想为$ 2 $，以$ q $为$ q $。最终的应用程序是在$ \ mathbb {f} _q [u] $中使用Primes的跟踪功能的总和。
We establish cancellation in short sums of certain special trace functions over $\mathbb{F}_q[u]$ below the Pólya-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 Möbius 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 $\mathbb{F}_q[u]$.
