Title: Finite monodromy of some two-parameter families of exponential sums Show Chinese title

Title: 某些双参数指数和族的有限单值性

Abstract: We determine the set of polynomials $f(x)\in k[x]$, where $k$ is a finite field, such that the local system on $\mathbb G_m^2$ which parametrizes the family of exponential sums $(s,t)\mapsto\sum_{x\in k}\psi(sf(x)+tx)$ has finite monodromy, in two cases: when $f(x)=x^d+\lambda x^e$ is a binomial and when $f(x)=(x-\alpha)^d(x-\beta)^e$ is of Belyi type. Show Chinese abstract

Abstract: 我们确定多项式$f(x)\in k[x]$的集合，其中$k$是一个有限域，使得在$\mathbb G_m^2$上参数化指数和族$(s,t)\mapsto\sum_{x\in k}\psi(sf(x)+tx)$的局部系统具有有限单值群，在两种情况下：当$f(x)=x^d+\lambda x^e$是二项式时，以及当$f(x)=(x-\alpha)^d(x-\beta)^e$是 Belyi 类型时。