论文标题
关于多元雅各比总和的分布
On the distribution of multivariate Jacobi sums
论文作者
论文摘要
令$ \ mathbf {f} _q $为$ q $元素的有限字段。我们表明，标准化的jacobi sum $ q^{ - （m-1）/2} \ Mathcal {a} _m $通过$ \ MathBf {f} _Q^\ times $的$ \ MathBf {f} _Q^\ times $的任意集运行（\ log q）^{\ frac {1}δ-1} $ for $ε>δ>δ> 0 $固定，$ q \ to \ infty $或者如果$ \＃\＃\ m athcal {a} _1 _1 \＃\ m rathcal {a} _2/q \ to \ \ \ to \ frac {\ q \ firce \ frac {\ q \ to \ infty $。这扩展了XI，Z. Zheng和作者的先前结果。
Let $\mathbf{F}_q$ be a finite field of $q$ elements. We show that the normalized Jacobi sum $q^{-(m-1)/2}J(χ_1,\dots,χ_m)$ ($χ_1\dotsm χ_m$ nontrivial) is asymptotically equidistributed on the unit circle, when $χ_1\in \mathcal{A}_1,\dots, χ_m\in \mathcal{A}_m$ run through arbitrary sets of nontrivial multiplicative characters of $\mathbf{F}_q^\times$, if $\#\mathcal{A}_1\ge q^{\frac{1}{2}+ε}$, $\#\mathcal{A}_2 \ge (\log q)^{\frac{1}δ-1}$ for $ε>δ>0$ fixed and $q\to \infty$ or if $\#\mathcal{A}_1\#\mathcal{A}_2/q\to \infty$. This extends previous results of Xi, Z. Zheng, and the authors.
