Schriftenverzeichnis

1

Mehrklassige Geschlechter von Einheitsformen in total reellen algebraischen Zahlkörpern, J. Reine Angew. Math. 262/263 (1973), 420-435.

2

Berechnung kleiner Diskriminanten total reeller algebraischer Zahlkörper, J. Reine Angew. Math. 278/279 (1975), 278-300.

3

Berechnung unabhängiger Einheiten und Klassenzahlen in total reellen biquadratischen Zahlkörpern, Computing 14 (1975), 67-78.

4

Über biquadratische Zahlkörper gleicher Diskriminante, Abh. Math. Sem. Univ. Hamb. 43 (1975), 192-197.

5

Invarianten des total reellen Körpers siebten Grades mit Minimaldiskriminante, Acta Arithmetica 30 (1976), 199-207.

6

A program for determining fundamental units, in Proc. 1976 ACM Symposium on Symbolic and Algebraic Computation, 235-240.

7

The minimum discriminant of seventh degree totally real algebraic number fields, in Number Theory and Algebra ed. by H. Zassenhaus, Academic Press 1977, 235-240.

8

(mit W. Plesken) On maximal finite irreducible subgroups of GL(n,${\cal Z}$), I. The five and seven dimensional case, Math. Comp. 31 (1977), 536-551.

9

(mit W. Plesken) On maximal finite irreducible subgroups of GL(n,${\cal Z}$), II. The six dimensional case, Math. Comp. 31 (1977), 552-573.

10

(mit H. Zassenhaus) An effective number geometric method of computing the fundamental units of an algebraic number field, Math. Comp. 31 (1977), 754-770.

11

Regulatorabschätzungen für total reelle algebraische Zahlkörper, J. Number Theory 9 (1977), 459-492.

12

Eine Regulatorabschätzung, Abh. Math. Sem. Univ. Hamb. 47 (1978), 95-106.

13

(mit H. Zassenhaus) On unit computation in real quadratic fields, in Symbolic and Algebraic Computation, Springer Lect. Notes in Comp. Sc. 72 (1979), 140-152.

14

(mit W. Plesken) On maximal finite irreducible subgroups of GL(n,${\cal Z}$), III. The nine dimensional case, Math. Comp. 34 (1980), 245-258.

15

(mit W. Plesken) On maximal finite irreducible subgroups of GL(n,${\cal Z}$), IV. Remarks on even dimensions with applications to n=8, Math. Comp. 34 (1980), 259-275.

16

(mit W. Plesken) On maximal finite irreducible subgroups of GL(n,${\cal Z}$), V. The eight dimensional case and a complete description of dimensions less than ten, Math. Comp. 34 (1980), 277-301.

17

On the computation of lattice vetors of minimal length, successive minima and reduced bases with applications, ACM SIGSAM Bulletin 15 (1981), 37-44.

18

(mit D. Y. Y. Yun) On solving systems of algebraic equations via ideal bases and elimination theory, in Proc. 1981 ACM Symposium on Symbolic and Algebraic Computation, 206-211.

19

On the computation of number fields of small discriminants including the minimum discriminants of sixth degree fields, J. Number Theory 14 (1982), 99-117.

20

(mit H. Zassenhaus) On effective computation of fundamental units I, Math. Comp. 38 (1982), 275-291.

21

(mit P. Weiler und H. Zassenhaus) On effective computation of fundamental units II, Math. Comp. 38 (1982), 293-329.

22

On the determination of algebraic number fields of given discriminant, in Computer Algebra, Springer Lect. Notes in Comp. Sc. 144 (1982), 71-76.

23

Computation of integral solutions of a special type of systems of quadratic equations, in Computer Algebra, Springer Lect. Notes in Comp. Sc. 162 (1983), 203-213.

24

(mit U. Fincke) A procedure for determining algebraic integers of given norm, in Computer Algebra, Springer Lect. Notes in Comp. Sc. 162 (1983), 194-202.

25

(mit U. Fincke) On reduction algorithms in non linear mathematical programming, in DGOR Operations Research Proc. 83, Springer Verlag 1983, 289-295.

26

On constructive methods in algebraic number theory, in Coll. Math. Soc. János Bolyai 34, Topics in Classical Number Theory, Elsevier North Holland 1984, 1251-1263.

27

(mit U. Fincke) Improved methods for calculating vectors of short length in a lattice, including a complexity analysis, Math. Comp. 44 (1985), 463-471.

28

(mit W. Plesken) Constructing integral lattices with prescribed minimum I, Math. Comp. 45 (1985), 209-221 und S5-S16.

29

(mit U. Fincke) A new method of computing fundamental units in algebraic number fields, Proc. EUROCAL`85, Springer Lect. Notes in Comp. Sc. 204 (1985), 470-478.

30

(mit H. Zassenhaus) Über die Berechnung von Klassenzahlen und Klassengruppen algebraischer Zahlkörper, J. Reine Angew. Math. 361 (1985), 50-72.

31

Über zahlengeometrische Methoden in der Konstruktiven Algebraischen Zahlentheorie, Bericht Nr. 270 (1986), Math.-Stat. Sekt., Forsch.ges. Joanneum, Graz, 23 pp..

32

On computing isomorphisms of equation orders, Math. Comp. 48 (1987), 309-314.

33

A modification of the LLL-algorithm, J. Symbolic Computation 4 (1987), 123-127.

34

Zur Faktorisierung großer Zahlen, Der math. u. naturwiss. Unterricht, Jahrgang 41 (1988), 335-339.

35

Three principal tasks of computational algebraic number theory, in Number Theory and Applications, ed. by R. A. Mollin, NATO ASI, Ser. C: Math'l and Physic'l Sciences, vol. 265, Kluwer Acad. Publ. 1989, 279-324.

36

(mit J. Buchmann) On the complexity of computing class groups of algebraic number fields, in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Proceedings AAECC-6, Springer Lect. Notes in Comp. Sc. 357 (1989), 122-131.

37

(mit J. Buchmann) Computing a lattice basis from a system of generators, in Proc. EUROCAL'87, Springer Lect. Notes in Comp. Sc. 378 (1989), 54-63.

38

(mit J.Buchmann und J. von Schmettow) On the computation of unit groups and class groups of totally real quartic fields, Math. Comp. 53 (1989), 387-397.

39

(mit J. Martinet und F. Diaz y Diaz) The Minimum Discriminant of Totally Real Octic Fields, J. Number Theory 36 (1990), 145-159.

40

(mit U. Halbritter) On the computation of the Values of the Zeta Functions of Totally Real Cubic Fields, J. Number Theory 36 (1990), 266-288.

41

(mit I. Gaál und A. Pethö) On the Resolution of Index Form Equations in Biquadratic Number Fields I, J. Number Theory 38 (1991), 18-34.

42

(mit I. Gaál und A. Pethö) On the Resolution of Index Form Equations in Biquadratic Number Fields II, J. Number Theory 38 (1991), 35-51.

43

A note on index divisors, in Computational Number Theory, ed. by A. Pethö, M. E. Pohst, H. C. Williams, H. G. Zimmer, Walter de Gruyter 1991, 173-182.

44

(mit W. Bosma) Computations with finitely generated modules over Dedekind rings, in Proc. ISSAC'91 ed. by M. Watt, ACM Press, New York 1991, 151-156.

45

(mit I. Gaál und A. Pethö) On the resolution of index form equations, in Proc. ISSAC'91 ed. by M. Watt, ACM Press, New York 1991, 185-186.

46

(mit I. Gaál und A. Pethö) On the indices of biquadratic number fields with Galois group $V_4$ , Arch. Math. 57 (1991), 357-361.

47

Some aspects of computational algebraic number theory, in Proc. of the Int. Conf. on Algebra honoring A. Malcev, ed. by L. A. Bokut, Yu. L. Ershov, O. H. Kegel, and A. I. Kostríkin, Contemporary Mathematics 131 (1992), 461-474.

48

(mit D. Ford), The totally real $A_5$ extension of degree 6 with minimum discriminant, Exper. Math. 1 (1992), 231-235.

49

(mit J. von Schmettow) On the computation of unit groups and class groups of totally complex quartic fields, Math. Comp. 60 (1993), 793-800.

50

(mit W. Plesken), Constructing integral lattices with prescribed minimum II, Math. Comp. 60 (1993), 817-825.

51

(mit J. Buchmann und D. Ford) Enumeration of Quartic Fields of Small Discriminant, Math. Comp. 61 (1993), 873-879.

52

(mit D. Ford), The totally real $A_6$ extension of degree 6 with minimum discriminant, Exper. Math. 2 (1993), 231-232.

53

(mit I. Gaál und A. Pethö) On the resolution of index form equations in quartic number fields , J. Symb. Comp. 16 (1993), 563-584.

54

In Memoriam: Hans Zassenhaus, J. Number Theory 47 (1994), 1-12.

55

On computing fundamental units, J. Number Theory 47 (1994), 93-105.

56

(mit J. Buchmann und J. von Schmettow) On Unit Groups and Class Groups of Quartic Fields of Signature (2,1), Math. Comp. 62 (1994), 387-390.

57

(mit A. Schwarz und F. Diaz y Diaz), A Table of Quintic Fields, Math. Comp. 63 (1994), 361-376.

58

(mit J. Buchmann und M. Jüntgen), A Practical Version of the Generalized Lagrange Algorithm, Exper. Math. 3 (1994), 199-207.

59

(mit I. Gaál und A. Pethö) On the Resolution of Index Form Equations in Dihedral Quartic Number Fields, Exper. Math. 3 (1994), 245-254.

60

(mit M. Daberkow) Computations with relative extensions of number fields with an application to the construction of Hilbert class fields, in Proc. ISSAC'95 ed. by A. H. M. Levelt, ACM Press, New York 1995, 68-76.

61

(mit I. Gaál und A. Pethö) On the Resolution of Index Form Equations in Biquadratic Number Fields III, J. Number Theory 53 (1995), 100-114.

62

(mit I. Gaál und A. Pethö) Simultaneous representation of integers by a pair of ternary quadratic forms - with an application to index form equations in quartic number fields, J. Number Theory 57 (1996), 90-104.

63

(mit M. Daberkow) On integral bases in relative quadratic extensions, Math. Comp. 65 (1996), 319-329.

64

Computational aspects of Kummer theory, in Algorithmic Number Theory ed. by H. Cohen, Springer Lect. Notes in Comp. Sc. 1122 (1996), 259-272.

65

(mit M. Daberkow) On computing Hilbert class fields of prime degree, in Algorithmic Number Theory ed. by H. Cohen, Springer Lect. Notes in Comp. Sc. 1122 (1996), 67-74.

66

(mit C. Fieker) On lattices in relative extensions, in Algorithmic Number Theory ed. by H. Cohen, Springer Lect. Notes in Comp. Sc. 1122 (1996), 133-139.

67

(mit M. Schörnig) On computing invariants of function fields, in Algorithmic Number Theory ed. by H. Cohen, Springer Lect. Notes in Comp. Sc. 1122 (1996), 273-282.

68

Computing Invariants of Algebraic Number Fields, in Group Theory, Algebra, and Number Theory ed. by H. G. Zimmer, de Gruyter 1996, 53-73.

69

(mit I. Gaál) On the Resolution of Index Form Equations in Sextic Fields with an Imaginary Quadratic Subfield, J. Symb. Comp. 22 (1996), 425-434.

70

(mit C. Fieker und A. Jurk) On solving relative norm equations in algebraic number fields, Math. Comp. 66 (1997), 399-410.

71

(mit J. Klüners) On computing subfields, J. Symb. Comp. 24 (1997), 385-397.

72

(mit M. Daberkow, C. Fieker, J. Klüners, K. Roegner, M. Schörnig, and K. Wildanger) KANT V4, in J. Symb. Comp. 24 (1997), 267-283.

73

On validated computing in algebraic number fields, J. Symb. Comp. 24 (1997), 657-665.

74

(mit I. Gaál) Power integral bases in a parametric family of totally real cyclic quintics, Math. Comp. 66 (1997), 1689-1696.

75

(mit K. Wildanger) A table of unit groups and class groups of quintic fields and a regulator bound, Math. Comp. 67 (1998), 361-367.

76

(mit M. Daberkow) On the Computation of Hilbert Class Fields, J. Number Theory 69 (1998), 213-230.

77

(mit D. Ford, M. Daberkow und N. Haddad) The $S_5$ Extensions of degree 6 with minimum discriminant, Exper. Math. 7 (1998), 121-124.

77

From class groups to class fields, pp. 103-119 in ``Algorithmic Algebra and Number Theory'', eds. B.H. Matzat, G.-M. Greuel, G. Hiss, Springer-Verlag Berlin Heidelberg 1999.

78

(mit S. Pauli) On the computation of the multiplicative group of residue class rings, submitted to Math. Comp..

79

Factoring polynomials over global fields, submitted to J. Symb. Comp..

80

(mit I. Gaál) On the resolution of relative Thue equations, submitted to Math. Comp..

81

(mit I. Gaál) Computing power integral bases in octic fields with a quadratic subfield, submitted to J. Number Theory.

Bücher

1. (als Herausgeber) $Algorithmic \ Methods \ in \ Algebra \ and \ Number \ Theory$, Academic Press 1988.

2. (mit H. Zassenhaus) $Algorithmic \ Algebraic \ Number \ Theory$, Cambridge Univ. Press 1989.
First Paperback edition 1997 (contains additional chapter on recent developments).

3. (als Herausgeber mit A. Pethö, H. C. Williams und H. G. Zimmer) $Computational \ Number \ Theory$, Walter de Gruyter 1991.

4. $Computational \ Algebraic \ Number \ Theory$, DMV Seminar 21, Birkhäuser Verlag 1993.