We tabulate polynomials in Q[t] with a given factorization partition, bad reduction entirely within a given set of primes, and satisfying auxiliary conditions associated to 0, 1, and ∞. We explain how these polynomials are of particular interest because of their role in the construction of nonsolvable number fields of arbitrarily large degree and bounded ramification.
Bibliographical noteFunding Information:
We thank Michael Bennett, Frits Beukers, John Cremona, John Jones, Akshay Venkatesh, and especially the anonymous referee for comments helpful to this paper. We thank the Simons Foundation for research support through grant #209472.
- number field