Among other work, he gave explicit bounds for the Chebotarev density theorem, which imply that if one assumes the generalized Riemann hypothesis then   is generated by its elements smaller than  2(log n)2. This result shows that the generalized Riemann hypothesis implies tight bounds for the necessary run-time of the deterministic version of the Miller–Rabin primality test.
Aside from his other accomplishments, he established clear boundaries for the Chebotarev density theorem, which suggest that if one assumes the generalized Riemann hypothesis then  can be generated by its elements smaller than 2(log n)2. This finding shows that the generalized Riemann hypothesis implies a tight time limit for the deterministic version of the Miller–Rabin primality test.