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$\DeclareMathOperator\bias{bias}$I'm trying to figure out how to approach the following question: Let $g$, $h$ be polynomials over $\mathbb{Z}_p$ (for prime $p$) with $n>1$ variables. Denote by $\...

I encounter a tricky sum like the Kloosterman sum $${\sum_{x \mod P}}^\ast e\left(\frac{ax+\overline{x}}{P}+\frac{lx^2}{P^2}\right),$$ where $l$ is a positive integer co-prime with $P$ and here $P$ ...

At every $n\in\mathbb N$ (all polynomials are of degree $O(1)$) is there $g_{3,1}^{(n)},\dots,g_{3,k}^{(n)}\in\mathbb F_3[x_1,\dots,x_n]$ at $k=\mathsf{poly}(n)$ and $g_2^{(n)}\in\mathbb F_2[x_1,\dots,...

There is a basic question regrading the 3-dimensional hyper-Kloosterman sum which needs some help from the experts here: For any integers $q,h \in \mathbb{N}$, how to estimate the sum: $$\sideset{_{}^{...