Displaying similar documents to “Explicit construction of integral bases of radical function fields”

Constructing class fields over local fields

Sebastian Pauli (2006)

Journal de Théorie des Nombres de Bordeaux

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Let K be a 𝔭 -adic field. We give an explicit characterization of the abelian extensions of K of degree p by relating the coefficients of the generating polynomials of extensions L / K of degree p to the exponents of generators of the norm group N L / K ( L * ) . This is applied in an algorithm for the construction of class fields of degree p m , which yields an algorithm for the computation of class fields in general.

Small generators of function fields

Martin Widmer (2010)

Journal de Théorie des Nombres de Bordeaux

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Let 𝕂 / k be a finite extension of a global field. Such an extension can be generated over k by a single element. The aim of this article is to prove the existence of a ”small” generator in the function field case. This answers the function field version of a question of Ruppert on small generators of number fields.

Absolute norms of p -primary units

Supriya Pisolkar (2009)

Journal de Théorie des Nombres de Bordeaux

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We prove a local analogue of a theorem of J. Martinet about the absolute norm of the relative discriminant ideal of an extension of number fields. The result can be seen as a statement about 2 -primary units. We also prove a similar statement about the absolute norms of p -primary units, for all primes p .

Thomas’ conjecture over function fields

Volker Ziegler (2007)

Journal de Théorie des Nombres de Bordeaux

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Thomas’ conjecture is, given monic polynomials p 1 , ... , p d ∈ ℤ [ a ] with 0 < deg p 1 < ⋯ < deg p d , then the Thue equation (over the rational integers) ( X - p 1 ( a ) Y ) ⋯ ( X - p d ( a ) Y ) + Y d = 1 has only trivial solutions, provided a ≥ a 0 with effective computable a 0 . We consider a function field analogue of Thomas’ conjecture in case of degree d = 3 . Moreover we find a counterexample to Thomas’ conjecture for d = 3 .

Computation of 2-groups of positive classes of exceptional number fields

Jean-François Jaulent, Sebastian Pauli, Michael E. Pohst, Florence Soriano–Gafiuk (2008)

Journal de Théorie des Nombres de Bordeaux

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We present an algorithm for computing the 2-group 𝒞 ℓ F p o s of the positive divisor classes in case the number field F has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel W K 2 ( F ) in K 2 ( F ) .