@article{34846, abstract = {{Given a field extension K/k of degree n we are interested in finding the subfields of K containing k. There can be more than polynomially many subfields. We introduce the notion of generating subfields, a set of up to n subfields whose intersections give the rest. We provide an efficient algorithm which uses linear algebra in k or lattice reduction along with factorization in any extension of K. Implementations show that previously difficult cases can now be handled.}}, author = {{van Hoeij, Mark and Klüners, Jürgen and Novocin, Andrew}}, issn = {{0747-7171}}, journal = {{Journal of Symbolic Computation}}, keywords = {{Computational Mathematics, Algebra and Number Theory}}, pages = {{17--34}}, publisher = {{Elsevier BV}}, title = {{{Generating subfields}}}, doi = {{10.1016/j.jsc.2012.05.010}}, volume = {{52}}, year = {{2011}}, } @article{34887, abstract = {{Let d be a nonsquare positive integer. We give the value of the natural probability that the narrow ideal class groups of the quadratic fields ℚ(√d) and ℚ(√−d) have the same 4-ranks. }}, author = {{Fouvry, Étienne and Klüners, Jürgen}}, issn = {{1937-0652}}, journal = {{Algebra & Number Theory}}, keywords = {{Algebra and Number Theory}}, number = {{5}}, pages = {{493--508}}, publisher = {{Mathematical Sciences Publishers}}, title = {{{On the Spiegelungssatz for the 4-rank}}}, doi = {{10.2140/ant.2010.4.493}}, volume = {{4}}, year = {{2010}}, } @article{34889, abstract = {{We prove that van Hoeij’s original algorithm to factor univariate polynomials over the rationals runs in polynomial time, as well as natural variants. In particular, our approach also yields polynomial time complexity results for bivariate polynomials over a finite field.}}, author = {{Belabas, Karim and van Hoeij, Mark and Klüners, Jürgen and Steel, Allan}}, issn = {{1246-7405}}, journal = {{Journal de Théorie des Nombres de Bordeaux}}, keywords = {{Algebra and Number Theory}}, number = {{1}}, pages = {{15--39}}, publisher = {{Cellule MathDoc/CEDRAM}}, title = {{{Factoring polynomials over global fields}}}, doi = {{10.5802/jtnb.655}}, volume = {{21}}, year = {{2009}}, } @inproceedings{11935, abstract = {{The generalized sidelobe canceller by Griffith and Jim is a robust beamforming method to enhance a desired (speech) signal in the presence of stationary noise. Its performance depends to a high degree on the construction of the blocking matrix which produces noise reference signals for the subsequent adaptive interference canceller. Especially in reverberated environments the beamformer may suffer from signal leakage and reduced noise suppression. In this paper a new blocking matrix is proposed. It is based on a generalized eigenvalue problem whose solution provides an indirect estimation of the transfer functions from the source to the sensors. The quality of the new generalized eigenvector blocking matrix is studied in simulated rooms with different reverberation times and is compared to alternatives proposed in the literature.}}, author = {{Warsitz, Ernst and Krueger, Alexander and Haeb-Umbach, Reinhold}}, booktitle = {{IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2008)}}, keywords = {{adaptive interference canceller, adaptive signal processing, array signal processing, beamforming method, eigenvalues and eigenfunctions, generalized eigenvector blocking matrix, generalized sidelobe canceller, interference suppression, matrix algebra, noise suppression, speech enhancement, transfer function estimation, transfer functions}}, pages = {{73--76}}, title = {{{Speech enhancement with a new generalized eigenvector blocking matrix for application in a generalized sidelobe canceller}}}, doi = {{10.1109/ICASSP.2008.4517549}}, year = {{2008}}, } @article{39947, author = {{Rösler, Margit}}, issn = {{0010-437X}}, journal = {{Compositio Mathematica}}, keywords = {{Algebra and Number Theory}}, number = {{03}}, pages = {{749--779}}, publisher = {{Wiley}}, title = {{{Bessel convolutions on matrix cones}}}, doi = {{10.1112/s0010437x06002594}}, volume = {{143}}, year = {{2007}}, } @article{34891, abstract = {{We study the asymptotics conjecture of Malle for dihedral groups Dℓ of order 2ℓ, where ℓ is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen--Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds. }}, author = {{Klüners, Jürgen}}, issn = {{1246-7405}}, journal = {{Journal de Théorie des Nombres de Bordeaux}}, keywords = {{Algebra and Number Theory}}, number = {{3}}, pages = {{607--615}}, publisher = {{Cellule MathDoc/CEDRAM}}, title = {{{Asymptotics of number fields and the Cohen–Lenstra heuristics}}}, doi = {{10.5802/jtnb.561}}, volume = {{18}}, year = {{2006}}, } @article{34892, abstract = {{We prove that the number of quartic S4--extensions of the rationals of given discriminant d is $O_\eps(d^{1/2+\eps})$ for all $\eps>0$. For a prime number p we derive that the dimension of the space of octahedral modular forms of weight 1 and conductor p or p² is bounded above by O(p¹/²log(p)²). }}, author = {{Klüners, Jürgen}}, issn = {{0065-1036}}, journal = {{Acta Arithmetica}}, keywords = {{Algebra and Number Theory}}, number = {{2}}, pages = {{185--194}}, publisher = {{Institute of Mathematics, Polish Academy of Sciences}}, title = {{{The number of S₄-fields with given discriminant}}}, doi = {{10.4064/aa122-2-3}}, volume = {{122}}, year = {{2006}}, } @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}}, } @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}}, } @inproceedings{39421, abstract = {{We present a rigorous but transparent semantics definition of SystemC that covers method, thread, and clocked thread behavior as well as their interaction with the simulation kernel process. The semantics includes watching statements, signal assignment, and wait statements as they are introduced in SystemC V1.O. We present our definition in form of distributed Abstract State Machines (ASMs) rules reflecting the view given in the SystemC User's Manual and the reference implementation. We mainly see our formal semantics as a concise, unambiguous, high-level specification for SystemC-based implementations and for standardization. Additionally, it can be used as a sound basis to investigate SystemC interoperability with Verilog and VHDL.}}, author = {{Müller, Wolfgang and Ruf, Jürgen and Hoffmann, D. W. and Gerlach, Joachim and Kropf, Thomas and Rosenstiehl, W.}}, booktitle = {{Proceedings of the Design, Automation, and Test in Europe (DATE’01)}}, isbn = {{0-7695-0993-2}}, keywords = {{Yarn, Formal verification, Kernel, Hardware design languages, Electronic design automation and methodology, Algebra, Computational modeling, Logic functions, Computer languages, Clocks}}, publisher = {{IEEE}}, title = {{{The Simulation Semantics of SystemC}}}, doi = {{10.1109/DATE.2001.915002}}, 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{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}}, }