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Full-Text Articles in Number Theory
Polynomials With Prescribed Bad Primes, David P. Roberts
Polynomials With Prescribed Bad Primes, David P. Roberts
Mathematics Publications
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.
The Tame-Wild Principle For Discriminant Relations For Number Fields, John W. Jones, David P. Roberts
The Tame-Wild Principle For Discriminant Relations For Number Fields, John W. Jones, David P. Roberts
Mathematics Publications
Consider tuples ( K1 , … , Kr ) of separable algebras over a common local or global number field F1, with the Ki related to each other by specified resolvent constructions. Under the assumption that all ramification is tame, simple group-theoretic calculations give best possible divisibility relations among the discriminants of Ki ∕ F . We show that for many resolvent constructions, these divisibility relations continue to hold even in the presence of wild ramification.