We design an algorithm for computing the $L$-series associated to an Anderson $t$-motives, exhibiting quasilinear complexity with respect to the target precision. Based on experiments, we conjecture that the order of vanishing at $T=1$ of the $v$-adic $L$-series of a given Anderson $t$-motive with good reduction does not depend on the finite place $v$.

翻译：我们设计了一种算法，用于计算与Anderson $t$-动机相关的$L$-级数，该算法相对于目标精度具有拟线性复杂度。基于实验，我们推测，对于具有良好约化的给定Anderson $t$-动机，其$v$-进$L$-级数在$T=1$处的消失阶数与有限位$v$无关。