Let $f(x)=x^n+a_{n-1}x^{n-1}+dots+a_0$ $(a_{n-1},dots,a_0inmathbb Z)$ be a polynomial with complex roots $lpha_1,dots,lpha_n$ and suppose that a linear relation over $mathbb Q$ among $1,lpha_1,dots,lpha_n$ is a? multiple of $sum_ilpha_i+a_{n-1}=0$ only. For a prime number $p$ such that $f(x)mod p$ has $n$ distinct integer? roots $0&r_1&dots&r_n&p$, we proposed in a previous paper a conjecture that the sequence of points $(r_1/p,dots,r_n/p)$ is equi-distributed in some sense. In this paper, we show that it implies the equi-distribution of the sequence of $r_1/p,dots,r_n/p$ in the ordinary sense and give the expected density of primes satisfying $r_i/p&a$ for a fixed suffix $i$ and $0&a&1$.
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机译：设$ f（x）= x ^ n + a_ {n-1} x ^ {n-1} + dots + a_0 $ $（a_ {n-1}， dots，a_0 in mathbb Z）$是具有复杂根$ alpha_1， dots， alpha_n $的多项式，并假设$ 1， alpha_1， dots， alpha_n $中$ mathbb Q $的线性关系是a？仅$ sum_i alpha_i + a_ {n-1} = 0 $的倍数。对于质数$ p $使得$ f（x） bmod p $具有$ n $个不同的整数？根$ 0 展开▼
