标题： 秩2德林模块不变量的除数计数函数的正常顺序 显示英文标题

标题： The normal order of of the divisor-counting function for invariants of rank 2 Drinfeld modules

摘要： 我们计算了欧拉-庞加莱示性数和具有非平凡自同态环的2阶德林费尔德模在模$p$的约化中的弗罗贝尼乌斯迹的除数计数函数的一阶和二阶矩，当素数$p$在德林费尔德模的普通约化素数中变化时。从这些矩中，我们推导出这些不变量的素数因子数的正则顺序。 显示英文摘要

摘要： We compute the first and second moments of the divisor-counting function for the Euler-Poincar\'{e} characteristic and the trace of Frobenius for the reductions modulo $p$ of a rank 2 Drinfeld module with nontrivial endomorphism ring, as the prime $p$ varies over the primes of ordinary reduction of the Drinfeld module. From these moments we derive the normal order of the number of prime divisors of these invariants.