Polynomials with prescribed bad primes

David P. Roberts

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    1 Scopus citations

    Abstract

    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
    Volume11
    Issue number4
    DOIs
    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.

    Keywords

    • Polynomial
    • discriminant
    • number field
    • ramification

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