一句话：证明根式恒等测试在 GRH 下属于 coNP，且平方根素数版本在 GRH 下属于 coRP、无条件属于 coNP。
本文研究根式恒等测试问题（RIT）：给定表示多项式的代数电路，以及用二进制写出的非负整数 a_i,d_i，判定该多项式是否在实根式 a_i^{1/d_i} 处取零。作者改进了由实数存在理论得到的 PSPACE 上界，在广义黎曼假设（GRH）下将 RIT 置于 coNP。对于受限版本 2-RIT（根式为二进制素数的平方根），此前仅知它至少与多项式恒等测试一样难，且上界不优于 PSPACE；本文证明其在 GRH 下属于 coRP，并无条件属于 coNP。证明依赖代数与解析数论定理，如 Chebotarev 密度定理和二次互反律。
We study the Radical Identity Testing problem (RIT): Given an algebraic circuit representing a polynomial and nonnegative integers a1, …, ak and d1, …, dk, written in binary, test whether the polynomial vanishes at the real radicals , i.e., test whether . We place the problem in coNP assuming the Generalised Riemann Hypothesis (GRH), improving on the straightforward PSPACE upper bound obtained by reduction to the existential theory of reals. Next we consider a restricted version, called 2-RIT, where the radicals are square roots of prime numbers, written in binary. It was known since the work of Chen and Kao [16] that 2-RIT is at least as hard as the polynomial identity testing problem, however no better upper bound than PSPACE was known prior to our work. We show that 2-RIT is in coRP assuming GRH and in coNP unconditionally. Our proof relies on theorems from algebraic and analytic number theory, such as the Chebotarev density theorem and quadratic reciprocity.