SIEVES AND THE MINIMAL RAMIFICATION PROBLEM

摘要

The minimal ramification problem may be considered as a quantitative version of the inverse Galois problem. For a nontrivial finite group G, let m.G/ be the minimal integer m for which there exists a G-Galois extension N/Q that is ramified at exactly m primes (including the infinite one). So, the problem is to compute or to bound m(G).