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：让$ f（x）= x ^ n + a_ {n-1} x ^ {n-1} + dots + a_0 $ $（a_ {n-1}， dots，a_0 in mathbb z）$ 是复杂根的多项式$ alpha_1， dots， alpha_n $，假设线性关系超过$ mathbb q $ 1， alpha_1， dots， alpha_n $是a？ $ sum_i alpha_i + a_ {n-1} = 0 $ off。 对于素数$ p $，使得$ f（x） bmod p $有$ n $ distinct整数？ ROOTS $ 0＆amp; r_1＆amp; dots＆amp; r_n＆amp; p $，我们在以前的纸张中提出了一个猜想，点数$（r_1 / p， dots，r_n / p）$ 在某种意义上分布。 在本文中，我们表明它意味着普通意义上的$ R_1 / P， DOTS，R_N / P $的序列的Equi分布，并给出满足$ r_i / p＆amp的预期素材密度; a $ 对于固定的后缀$ i $和$ 0＆amp; a＆amp; 1 $。
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