Polynomials with prescribed bad primes

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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.

Original languageEnglish (US)
Pages (from-to)1115-1148
Number of pages34
JournalInternational Journal of Number Theory
Issue number4
StatePublished - Jun 5 2015

Bibliographical note

Funding 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.

Publisher Copyright:
© 2015 World Scientific Publishing Company.


  • Polynomial
  • discriminant
  • number field
  • ramification


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