@article{34893,
  abstract     = {{Let K be a global field and O be an order of K. We develop algorithms for the computation of the unit group of residue class rings for ideals O in . As an application we show how to compute the unit group and the Picard group of O provided that we are able to compute the unit group and class group of the maximal order O of K.}},
  author       = {{Klüners, Jürgen and Pauli, Sebastian}},
  issn         = {{0021-8693}},
  journal      = {{Journal of Algebra}},
  keywords     = {{Algebra and Number Theory}},
  number       = {{1}},
  pages        = {{47--64}},
  publisher    = {{Elsevier BV}},
  title        = {{{Computing residue class rings and Picard groups of orders}}},
  doi          = {{10.1016/j.jalgebra.2005.04.013}},
  volume       = {{292}},
  year         = {{2005}},
}

@misc{42807,
  author       = {{Klüners, Jürgen}},
  isbn         = {{978-3-8322-4003-5}},
  pages        = {{114}},
  publisher    = {{Shaker Verlag}},
  title        = {{{Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)}}},
  year         = {{2005}},
}

@misc{43455,
  author       = {{Kirschmer, Markus}},
  pages        = {{147}},
  title        = {{{Konstruktive Idealtheorie in Quaternionenalgebren (Diplomarbeit)}}},
  year         = {{2005}},
}

@article{34896,
  abstract     = {{We apply class field theory to the computation of the minimal discriminants for certain solvable groups. In particular, we apply our techniques to small Frobenius groups and all imprimitive degree 8 groups such that the corresponding fields have only a degree 2 and no degree 4 subfield.}},
  author       = {{Fieker, Claus and Klüners, Jürgen}},
  issn         = {{0022-314X}},
  journal      = {{Journal of Number Theory}},
  keywords     = {{Algebra and Number Theory}},
  number       = {{2}},
  pages        = {{318--337}},
  publisher    = {{Elsevier BV}},
  title        = {{{Minimal discriminants for fields with small Frobenius groups as Galois groups}}},
  doi          = {{10.1016/s0022-314x(02)00071-9}},
  volume       = {{99}},
  year         = {{2003}},
}

@article{35954,
  abstract     = {{Let {\ASIE K}\,/{\small \ℚ}({\ASIE t \!}) be a finite extension. We describe algorithms for computing subfields and automorphisms of {\ASIE K}\,/{\small \ℚ}({\ASIE t }\!). As an application we give an algorithm for finding decompositions of rational functions in {\small \ℚ(α)}. We also present an algorithm which decides if an extension {\ASIE L}\,/{\small \ℚ}({\ASIE t \!}) is a subfield of {\ASIE K}. In case [{\ASIE K : \;}{\small\ℚ}({\ASIE t \!})] = [{\ASIE L : \;}{\small \ℚ}({\ASIE t \!})] we obtain a {\small \ℚ}({\ASIE t \!})-isomorphism test. Furthermore, we describe an algorithm which computes subfields of the normal closure of {\ASIE K}\,/{\small \ℚ}({\ASIE t \!}).}},
  author       = {{Klüners, Jürgen}},
  journal      = {{Experiment. Math. }},
  keywords     = {{algorithms, decompositions, Galois groups, subfields}},
  number       = {{2}},
  pages        = {{171--181}},
  publisher    = {{Elsevier BV}},
  title        = {{{Algorithms for function fields}}},
  volume       = {{11}},
  year         = {{2002}},
}

@article{34897,
  abstract     = {{This paper announces the creation of a database for number fields. It describes the contents and the methods of access, indicates the origin of the polynomials, and formulates the aims of this collection of fields.}},
  author       = {{Klüners, Jürgen and Malle, Gunter}},
  issn         = {{1461-1570}},
  journal      = {{LMS Journal of Computation and Mathematics}},
  keywords     = {{Computational Theory and Mathematics, General Mathematics}},
  pages        = {{182--196}},
  publisher    = {{Wiley}},
  title        = {{{A Database for Field Extensions of the Rationals}}},
  doi          = {{10.1112/s1461157000000851}},
  volume       = {{4}},
  year         = {{2001}},
}

@article{34900,
  abstract     = {{We describe methods for the computation of Galois groups of univariate polynomials over the rationals which we have implemented up to degree 15. These methods are based on Stauduhar’s algorithm. All computations are done in unramified p -adic extensions. For imprimitive groups we give an improvement using subfields. In the primitive case we use known subgroups of the Galois group together with a combination of Stauduhar’s method and the absolute resolvent method.}},
  author       = {{Geissler, Katharina and Klüners, Jürgen}},
  issn         = {{0747-7171}},
  journal      = {{Journal of Symbolic Computation}},
  keywords     = {{Computational Mathematics, Algebra and Number Theory}},
  number       = {{6}},
  pages        = {{653--674}},
  publisher    = {{Elsevier BV}},
  title        = {{{Galois Group Computation for Rational Polynomials}}},
  doi          = {{10.1006/jsco.2000.0377}},
  volume       = {{30}},
  year         = {{2000}},
}

@article{34901,
  abstract     = {{Let L = K(α) be an Abelian extension of degree n of a number field K, given by the minimal polynomial of α over K. We describe an algorithm for computing the local Artin map associated with the extension L / K at a finite or infinite prime v of K. We apply this algorithm to decide if a nonzero a ∈ K is a norm from L, assuming that L / K is cyclic.}},
  author       = {{Acciaro, Vincenzo and Klüners, Jürgen}},
  issn         = {{0747-7171}},
  journal      = {{Journal of Symbolic Computation}},
  keywords     = {{Computational Mathematics, Algebra and Number Theory}},
  number       = {{3}},
  pages        = {{239--252}},
  publisher    = {{Elsevier BV}},
  title        = {{{Computing Local Artin Maps, and Solvability of Norm Equations}}},
  doi          = {{10.1006/jsco.2000.0361}},
  volume       = {{30}},
  year         = {{2000}},
}

@article{34899,
  abstract     = {{We describe methods for the construction of polynomials with certain types of Galois groups. As an application we deduce that all transitive groups G up to degree 15 occur as Galois groups of regular extensions of ℚ (t), and in each case compute a polynomial f ∈ ℚ [ x ] with Gal(f)  = G.}},
  author       = {{Klüners, Jürgen and Malle, Gunter}},
  issn         = {{0747-7171}},
  journal      = {{Journal of Symbolic Computation}},
  keywords     = {{Computational Mathematics, Algebra and Number Theory}},
  number       = {{6}},
  pages        = {{675--716}},
  publisher    = {{Elsevier BV}},
  title        = {{{Explicit Galois Realization of Transitive Groups of Degree up to 15}}},
  doi          = {{10.1006/jsco.2000.0378}},
  volume       = {{30}},
  year         = {{2000}},
}

@article{34898,
  abstract     = {{We compute a polynomial with Galois group SL₂(11) over ℚ. Furthermore we prove that SL₂(11) is the Galois group of a regular extension of ℚ (t).}},
  author       = {{Klüners, Jürgen}},
  issn         = {{0747-7171}},
  journal      = {{Journal of Symbolic Computation}},
  keywords     = {{Computational Mathematics, Algebra and Number Theory}},
  number       = {{6}},
  pages        = {{733--737}},
  publisher    = {{Elsevier BV}},
  title        = {{{A Polynomial with Galois GroupSL2(11)}}},
  doi          = {{10.1006/jsco.2000.0380}},
  volume       = {{30}},
  year         = {{2000}},
}

@article{34902,
  abstract     = {{We present a new polynomial decomposition which generalizes the functional and homogeneous bivariate decomposition of irreducible monic polynomials in one variable over the rationals. With these decompositions it is possible to calculate the roots of an imprimitive polynomial by solving polynomial equations of lower degree.}},
  author       = {{Klüners, Jürgen}},
  issn         = {{0747-7171}},
  journal      = {{Journal of Symbolic Computation}},
  keywords     = {{Computational Mathematics, Algebra and Number Theory}},
  number       = {{3}},
  pages        = {{261--269}},
  publisher    = {{Elsevier BV}},
  title        = {{{On Polynomial Decompositions}}},
  doi          = {{10.1006/jsco.1998.0252}},
  volume       = {{27}},
  year         = {{1999}},
}

@article{35941,
  abstract     = {{Let L = ℚ(α) be an abelian number field of degree n. Most
algorithms for computing the lattice of subfields of L require the computation
of all the conjugates of α. This is usually achieved by factoring the minimal
polynomial mα(x) of α over L. In practice, the existing algorithms for factoring
polynomials over algebraic number fields can handle only problems of moderate
size. In this paper we describe a fast probabilistic algorithm for computing
the conjugates of α, which is based on p-adic techniques. Given mα(x) and a
rational prime p which does not divide the discriminant disc(mα(x)) of mα(x),
the algorithm computes the Frobenius automorphism of p in time polynomial
in the size of p and in the size of mα(x). By repeatedly applying the algorithm
to randomly chosen primes it is possible to compute all the conjugates of α.}},
  author       = {{Klüners, Jürgen and Acciaro, Vincenzo}},
  issn         = {{1088-6842}},
  journal      = {{Mathematics of Computation}},
  number       = {{227}},
  pages        = {{1179--1186}},
  publisher    = {{American Mathematical Society (AMS)}},
  title        = {{{Computing Automorphisms of Abelian Number Fields}}},
  volume       = {{68}},
  year         = {{1999}},
}

@article{34903,
  abstract     = {{The software packageKANT V4for computations in algebraic number fields is now available in version 4. In addition a new user interface has been released. We will outline the features of this new software package.}},
  author       = {{DABERKOW, M. and FIEKER, C. and Klüners, Jürgen and POHST, M. and ROEGNER, K. and SCHÖRNIG, M. and WILDANGER, K.}},
  issn         = {{0747-7171}},
  journal      = {{Journal of Symbolic Computation}},
  keywords     = {{Computational Mathematics, Algebra and Number Theory}},
  number       = {{3-4}},
  pages        = {{267--283}},
  publisher    = {{Elsevier BV}},
  title        = {{{KANT V4}}},
  doi          = {{10.1006/jsco.1996.0126}},
  volume       = {{24}},
  year         = {{1997}},
}

@article{34904,
  abstract     = {{The purpose of this article is to determine all subfields ℚ(β) of fixed degree of a given algebraic number field ℚ(α). It is convenient to describe each subfield by a pair (h,g) of polynomials in ℚ[t] resp. Z[t] such thatgis the minimal polynomial of β = h(α). The computations are done in unramifiedp-adic extensions and use information concerning subgroups of the Galois group of the normal closure of ℚ(α) obtained from the van der Waerden criterion.}},
  author       = {{Klüners, Jürgen and Pohst, Michael}},
  issn         = {{0747-7171}},
  journal      = {{Journal of Symbolic Computation}},
  keywords     = {{Computational Mathematics, Algebra and Number Theory}},
  number       = {{3-4}},
  pages        = {{385--397}},
  publisher    = {{Elsevier BV}},
  title        = {{{On Computing Subfields}}},
  doi          = {{10.1006/jsco.1996.0140}},
  volume       = {{24}},
  year         = {{1997}},
}

@phdthesis{42806,
  author       = {{Klüners, Jürgen}},
  pages        = {{93}},
  title        = {{{Über die Berechnung von Automorphismen und Teilkörpern algebraischer Zahlkörper (Dissertation)}}},
  year         = {{1997}},
}

@misc{42808,
  author       = {{Klüners, Jürgen}},
  pages        = {{91}},
  title        = {{{Über die Berechnung von Teilkörpern algebraischer Zahlkörper (Diplomarbeit)}}},
  year         = {{1995}},
}