AI 中文总结
该研究受镜像对称启发，通过多项式高斯和实现塞尔伯格特征和的几何化，结合埃文斯的结果得到有限域上$A_1$库仑分支指数和的显式公式。
AI 中文摘要
受镜像对称启发，我们研究$A_1$库仑分支的$\boldsymbol{\text{F}}_q$点上的指数和，证明其纤维结构由多项式高斯和支配，为埃文斯研究的塞尔伯格特征和提供几何实现；利用埃文斯的计算，我们得到库仑分支指数和的显式公式，将其表示为经典高斯和的乘积。
英文摘要
Motivated by mirror symmetry, we study exponential sums over the $\mathbb{F}_q$-points of the $A_1$ Coulomb branch. We show that their fiberwise structure is governed by polynomial Gauss sums, providing a geometric realization of Selberg character sums studied by Evans. Using Evans's evaluation, we obtain explicit formulas for the Coulomb-branch exponential sums as products of classical Gauss sums.
Comments19 pages
