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Appendix C: Tables

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Part of the book series: Graduate Texts in Mathematics ((GTM,volume 193))

Abstract

In this appendix, we group a number of tables related to the subject matter of this book.

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Bibliography

  1. L. Adleman and M.-D. Huang, editors, Algorithmic Number Theory Symposium ANTS-I, Lecture Notes in Comp. Sci. 877, Springer-Verlag (1994).

    Google Scholar 

  2. Y. Amice, Les nombres p-adiques, SUP/Le Mathématicien 14, Presses Universitaires de France (1975).

    Google Scholar 

  3. E. Artin and J. Tate, Class field theory, Benjamin, New York (1967).

    Google Scholar 

  4. G. Bachman, Introduction to p-adic numbers and valuation theory, Academic paperbacks, Acad. Press (1964).

    Google Scholar 

  5. E. Bach and J. Shallit, Factor refinement, J. Algorithms 15 (1993), 199–222.

    Article  MathSciNet  MATH  Google Scholar 

  6. E. Bach and J. Shallit, Algorithmic number theory. Volume 1: Efficient algorithms, MIT Press, Cambridge, MA (1996).

    Google Scholar 

  7. E. Bach, J. Sorenson, Explicit bounds for primes in residue classes, Math. comp. 65 (1996), 1717–1735.

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Baily, On the density of discriminants of quartic fields, J. reine angew. Math. 315 (1980), 190–210.

    MathSciNet  MATH  Google Scholar 

  9. C. Batut, K. Belabas, D. Bernardi, H. Cohen, and M. Olivier, User’s guide to Pari-GP version 2.x.x, available by anonymous ftp.

    Google Scholar 

  10. T. Becker and V. Weispfenning, Gröbner bases, a computational approach to commutative algebra, Graduate Texts in Math. 141, Springer-Verlag (1993).

    Google Scholar 

  11. K. Belabas, A fast algorithm to compute cubic fields, Math. comp. 66 (1997), 1213–1237.

    Article  MathSciNet  MATH  Google Scholar 

  12. K. Belabas, On the mean 3-rank of quadratic fields, Compositio Math., to appear.

    Google Scholar 

  13. K. Belabas, Variations sur un thème de Davenport et Heilbronn, Thesis, Universite Bordeaux I (1996).

    Google Scholar 

  14. A.-M. Bergé and J. Martinet, Notions relatives de régulateurs et de hauteurs, Acta Arith. 54 (1989), 155–170.

    MathSciNet  MATH  Google Scholar 

  15. A.-M. Bergé, J. Martinet, and M. Olivier, The computation of sextic fields with a quadratic subfield, Math. comp. 54 (1990), 869–884.

    Article  MathSciNet  MATH  Google Scholar 

  16. G. Birkhoff, Subgroups of Abelian groups, Proc. Lond. Math. Soc. (2) 38 (1934–5), 385–401.

    MathSciNet  Google Scholar 

  17. W. Bosma, J. Cannon and C. Playoust, The Magma algebra system I: The user language, J. Symb. Comput. 24 (1997), 235–265.

    Article  MathSciNet  MATH  Google Scholar 

  18. W. Bosma and M. Pohst, Computations with finitely generated modules over Dedekind rings, Proceedings ISSAC′ 91 (1991), 151–156.

    Google Scholar 

  19. N. Bourbaki, Algèbre Commutative, Chapitre VII, Hermann, Paris.

    Google Scholar 

  20. N. Bourbaki, Algèbre, Chapitre VIII, Hermann, Paris.

    Google Scholar 

  21. B. Braaksma, Asymptotic expansions and analytic continuations for a class of Barnes integrals, Compos. Math. 15 (1964), 239–341.

    MathSciNet  Google Scholar 

  22. J. Buchmann and D. Ford, On the computation of totally real quartic fields of small discriminant, Math. comp. 52 (1989), 161–174.

    Article  MathSciNet  MATH  Google Scholar 

  23. J. Buchmann, D. Ford, and M. Pohst, Enumeration of quartic fields of small discriminant, Math. comp. 61 (1993), 873–879.

    Article  MathSciNet  MATH  Google Scholar 

  24. J. Buhler, editor, Algorithmic Number Theory Symposium ANTS-III, Lecture Notes in comp. Sci. 1423, Springer-Verlag (1998).

    Google Scholar 

  25. L. Butler, Subgroup lattices and symmetric functions, Memoirs of the A.M.S. 539 (1994).

    Google Scholar 

  26. J. Cassels and A. Fröhlich, Algebraic Number Theory, Academic Press, London, New York (1967).

    MATH  Google Scholar 

  27. P. Cassou-Noguès and A. Jehanne, Parité du nombre de classes des S 4-extensions de ℚ et courbes elliptiques, J. Number Theory 57 (1996), 366–384.

    Article  MathSciNet  MATH  Google Scholar 

  28. S. Cavallar and F. Lemmermeyer, The Euclidean algorithm in cubic number fields, Number Theory (Eger, 1996), de Gruyter, Berlin (1998), 123–146.

    Google Scholar 

  29. C. Chevalley, Sur la théorie du corps de classe dans les corps finis et les corps locaux, J. Fac. Sci. Tokyo 2 (1933), 365–475.

    MATH  Google Scholar 

  30. H. Cohen, A Course in Computational Algebraic Number Theory (3rd corrected printing), Graduate Texts in Math. 138, Springer-Verlag (1996).

    Google Scholar 

  31. H. Cohen, Hermite and Smith normal form algorithms over Dedekind domains, Math. comp. 65 (1996), 1681–1699.

    Article  MathSciNet  MATH  Google Scholar 

  32. H. Cohen, editor, Algorithmic Number Theory Symposium ANTS-II, Lecture Notes in comp. Sci. 1122, Springer-Verlag (1996).

    Google Scholar 

  33. H. Cohen and F. Diaz y Diaz, A polynomial reduction algorithm, Sém. de Théorie des Nombres Bordeaux (Série 2) 3 (1991), 351–360.

    Article  MathSciNet  MATH  Google Scholar 

  34. H. Cohen, F. Diaz y Diaz, and M. Olivier, Subexponential algorithms for class group and unit computations, J. Symb. Comput. 24 (1997), 433–441.

    Article  MathSciNet  MATH  Google Scholar 

  35. H. Cohen, F. Diaz y Diaz, and M. Olivier, Computing ray class groups, conductors and discriminants, Math. comp. 67 (1998), 773–795.

    Article  MathSciNet  MATH  Google Scholar 

  36. H. Cohen, F. Diaz y Diaz, and M. Olivier, Imprimitive octic fields with small discriminant, Algorithmic Number Theory Symposium ANTS-III (J. Buhler, ed.), Lecture Notes in comp. Sci. 1423, Springer-Verlag (1998), 372–380.

    Google Scholar 

  37. H. Cohen, F. Diaz y Diaz, and M. Olivier, A table of totally complex number fields of small discriminants, Algorithmic Number Theory Symposium ANTS-III (J. Buhler, ed.), Lecture Notes in comp. Sci. 1423, Springer-Verlag (1998), 381–391.

    Google Scholar 

  38. H. Cohen, F. Diaz y Diaz, and M. Olivier, Computation of relative quadratic class groups, Algorithmic Number Theory Symposium ANTS-III (J. Buhler, ed.), Lecture Notes in comp. Sci. 1423, Springer-Verlag (1998), 433–440.

    Google Scholar 

  39. H. Cohen, F. Diaz y Diaz, and M. Olivier, Tables of octic fields containing a quartic subfield, Math. comp., to appear.

    Google Scholar 

  40. H. Cohen, F. Diaz y Diaz, and M. Olivier, Algorithmic Methods for Finitely Generated Abelian Groups, Proc. 2nd Magma Conference, J. Symb. Comput., to appear.

    Google Scholar 

  41. H. Cohen and X.-F. Roblot, Computing the Hilbert class field of real quadratic fields, Math. comp., to appear.

    Google Scholar 

  42. J.-H. Conway and N. Sloane, Sphere packings, lattices and groups (3rd ed.), Grundlehren der math. Wiss. 290, Springer-Verlag, New York (1999).

    Google Scholar 

  43. G. Cornell and M. Rosen, A note on the splitting of the Hilbert class fields, J. Number Theory 11 (1988), 152–158.

    Article  MathSciNet  Google Scholar 

  44. D. Cox, J. Little, and D. O’Shea, Ideals, varieties and algorithms. An introduction to computational algebraic geometry and commutative algebra, Undergraduate Texts in Math., Springer-Verlag, New York (1992).

    Google Scholar 

  45. J. Cremona, Reduction of cubic and quartic forms, LMS Journal of Computation and Math. 2 (1999), 62–92.

    MathSciNet  Google Scholar 

  46. M. Daberkow, Bestimmung relativer Ganzheitsbasen in relativquadratischen Zahlkörpern, Diplomarbeit, Universität Düsseldorf (1993).

    Google Scholar 

  47. M. Daberkow, Über die Bestimmung der ganzen Elemente in Radikalerweiterungen algebraischer Zahlkörper, Thesis, Technische Universität Berlin (1995).

    Google Scholar 

  48. M. Daberkow, C. Fieker, J. Klüners, M. Pohst, K. Roegner, M. Schörnig, and K. Wildanger, KANT V4, J. Symb. Comput. 24 (1997), 267–283.

    Article  MATH  Google Scholar 

  49. B. Datskowsky and D. J. Wright, Density of discriminants of cubic extensions, J. reine angew. Math. 386 (1988), 116–138.

    MathSciNet  Google Scholar 

  50. H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields (I), Bull. London Math. Soc. 1 (1969), 345–348.

    Article  MathSciNet  MATH  Google Scholar 

  51. H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields (II), Proc. Roy. Soc. London 322 (1971), 405–420.

    Article  MathSciNet  MATH  Google Scholar 

  52. C. Delaunay, work in progress.

    Google Scholar 

  53. F. Diaz y Diaz, A table of totally real quintic number fields, Math. Comp. 56 (1991), 801–808.

    Article  MathSciNet  MATH  Google Scholar 

  54. F. Diaz y Diaz and M. Olivier, Algorithmique algébrique dans les corps de nombres, Etats de la Recherche en Algorithmique Arithmétique, Bordeaux, Soc. Math. France (1995).

    Google Scholar 

  55. D. Dummit and B. Tangedal, Computing the leading term of an Abelian L-function, Algorithmic Number Theory Symposium ANTS-III (J. Buhler, ed.), Lecture Notes in Comp. Sci. 1423, Springer-Verlag (1998), 400–411.

    Google Scholar 

  56. Y. Eichenlaub and M. Olivier, Computation of Galois groups for polynomials with degree up to eleven, submitted.

    Google Scholar 

  57. C. Fieker, Computing class fields via the Artin map, J. Symb. Comput., submitted.

    Google Scholar 

  58. C. Fieker and M. Pohst, On lattices over number fields, Algorithmic Number Theory Symposium ANTS-II (H. Cohen, ed.), Lecture Notes in Comp. Sci. 1122, Springer-Verlag (1996), 133–139.

    Google Scholar 

  59. D. Ford, Enumeration of totally complex quartic fields of small discriminant, Computational Number Theory (1989) (A. Pethö, M. Pohst, H. C. Williams, and H. Zimmer, eds.), de Gruyter, Berlin and New York (1991), 129–138.

    Google Scholar 

  60. D. Ford and P. Letard, Implementing the Round Four maximal order algorithm, J. Theorie des Nombres Bordeaux 6 (1994), 39–80.

    Article  MathSciNet  MATH  Google Scholar 

  61. E. Friedmann, Hecke’s integral formula, Sém. de Théorie des Nombres de Bordeaux, Exposé No. 5 (1987–1988).

    Google Scholar 

  62. A. Fröhlich and M. Taylor, Algebraic number theory, Cambridge Studies in Adv. Math. 27, Cambridge Univ. Press (1991).

    Google Scholar 

  63. K. Geddes, S. Czapor, and G. Labahn, Algorithms for Computer Algebra, Kluwer Academic Publishers, Boston, Dordrecht, London (1992).

    Book  MATH  Google Scholar 

  64. K. Geissler, Zur Berechnung von Galoisgruppe, Diplomarbeit, Technische Universität Berlin (1997).

    Google Scholar 

  65. P. Gordan, Beweis, dass jede Covariante und Invariante einer binären Form eine ganze Funktion mit numerischen Coefficienten einer endlichen Anzahl solcher Formen ist, J. reine angew. Math. 69 (1868), 323–354.

    Article  Google Scholar 

  66. G. Gras, Théorie du corps de classes global, Faculté des Sciences de Besançon (1979–1980).

    Google Scholar 

  67. J. Hafner and K. McCurley, Asymptotically fast triangularization of matrices over rings, SIAM J. Comput. 20 (1991), 1068–1083.

    Article  MathSciNet  MATH  Google Scholar 

  68. F. Hajir and C. Maire, Tamely ramified towers and discriminant bounds for number fields, preprint.

    Google Scholar 

  69. D. Harbater, Galois groups with prescribed ramification, Arithmetic Geometry (N. Childress and J. Jones, eds.), Contemp. Math. 174, American Math. Soc. (1994), 35–60.

    Google Scholar 

  70. H. Hasse, Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, Teil 1: Klassenkörpertheorie, Teil 1a: Beweise zu Teil 1, Teil 2: Reziprozitätsgesetz, PhysicaVerlag (1965).

    Google Scholar 

  71. H. Hasse, Zahlentheorie, Akademie-Verlag GmbH (1949).

    Google Scholar 

  72. G. Havas and B. Majewski, Integer matrix diagonalization, J. Symb. Comput. 24 (1997), 399–408.

    Article  MathSciNet  MATH  Google Scholar 

  73. G. Havas, B. Majewski, and K. Matthews, Extended GCD and Hermite normal form algorithms via lattice basis reduction, Experiment. Math. 7 (1998), 125–136.

    MathSciNet  MATH  Google Scholar 

  74. E. Hecke, Lectures on the theory of algebraic numbers, Graduate Texts in Math. 77, Springer-Verlag, Berlin, Heidelberg, New York (1981).

    Google Scholar 

  75. A. Hoppe, Normal forms over Dedekind domains, efficient implementation in the computer algebra system KANT, Thesis, Technische Universität Berlin (1998).

    Google Scholar 

  76. G. Janusz, Algebraic number fields (2nd ed.), Graduate Studies in Math. 7, American Math. Soc. (1996).

    Google Scholar 

  77. J. Klüners, On computing subfields — A detailed description of the algorithm, J. Théorie des Nombres Bordeaux 10 (1998), 243–271.

    Article  MATH  Google Scholar 

  78. J. Klüners and M. Pohst, On computing subfields, J. Symb. Comput. 24 (1997), 385–397.

    Article  MATH  Google Scholar 

  79. N. Koblitz, p-adic numbers, p-adic analysis, and zeta-functions (2nd edition), Graduate Texts in Math. 58, Springer-Verlag, Berlin, Heidelberg, New York (1984).

    Google Scholar 

  80. S. Lang, Elliptic functions, Addison-Wesley, Reading, MA (1973).

    MATH  Google Scholar 

  81. S. Lang, Introduction to modular forms, Springer-Verlag, Berlin, Heidelberg, New York (1976).

    MATH  Google Scholar 

  82. S. Lang, Algebraic number theory (2nd ed.), Graduate Texts in Math. 110, Springer-Verlag, Berlin, Heidelberg, New York (1994).

    Google Scholar 

  83. A. F. Lavrik, On functional equations of Dirichlet functions, Math. USSR-Izvestija 1 (1967), 421–432.

    Article  Google Scholar 

  84. F. Lemmermeyer, The Euclidean algorithm in algebraic number fields, Expo. Math. 13 (1995), 385–416.

    MathSciNet  MATH  Google Scholar 

  85. P. Letard, Construction de corps de nombres de degré 7 et 9, Thesis, Université Bordeaux I (1995).

    Google Scholar 

  86. A. Leutbecher, Euclidean fields hairing a large Lenstra constant, Ann. Inst. Fourier 35 (1985), 83–106.

    Article  MathSciNet  MATH  Google Scholar 

  87. A. Leutbecher and G. Niklasch, On cliques of exceptional units and Lenstra’s construction of Euclidean fields, Number Theory, Proceedings Journées Arithmétiques, Ulm 1987 (H. Schlickewei and E. Wirsing, eds.), Lecture Notes in Math. 1380, Springer-Verlag (1989), 150–178.

    Google Scholar 

  88. D. A. Marcus, Number fields, Springer-Verlag, New York (1977).

    Book  MATH  Google Scholar 

  89. J. Martinet, Character theory and Artin L-functions, Algebraic number fields (A. Fröhlich, ed.), Academic Press, London (1977), 1–87.

    Google Scholar 

  90. J. Martinet, Petits discriminants des corps de nombres, Journées arithmétiques 1980 (J. V. Armitage, ed.), London Math. Soc. Lecture Notes Ser. 56 (1982), 151–193.

    Google Scholar 

  91. J. Martinet, Méthodes géométriques dans la recherche des petits discriminants, Prog. Math. 59, Birkhäuser, Boston (1985), 147–179.

    Google Scholar 

  92. J. Martinet, Une introduction à la théorie du corps de classes (notes de M. Olivier), Ecole doctorale de mathématiques de Bordeaux (1991).

    Google Scholar 

  93. J. Martinet, Les réseaux parfaits des espaces euclidiens, Masson, Paris (1996).

    Google Scholar 

  94. J. Martinet et J.-J. Payan, Sur les extensions cubiques non galoisiennes des rationnels et leur clôture galoisienne, Jour. reine angew. Math. 228 (1967), 15–37.

    MathSciNet  MATH  Google Scholar 

  95. P. Montgomery, Partial LLL reduction, personal communication.

    Google Scholar 

  96. J. Nakagawa, On the relations among the class numbers of binary cubic forms, Invent. Math. 134 (1998), 101–138.

    Article  MathSciNet  MATH  Google Scholar 

  97. N. Nakagoshi, The structure of the multiplicative group of residue classes modulo N+1, Nagoya Math. J. 73 (1979), 41–60.

    MathSciNet  Google Scholar 

  98. J. Neukirch, Class field theory, Grundlehren der math. Wiss. 280, Springer-Verlag (1986).

    Google Scholar 

  99. H. Niederreiter and C. Xing, Algebraic curves over finite fields with many rational points, Number Theory (Eger, 1996), de Gruyter, Berlin (1998), 423–443.

    Google Scholar 

  100. A. Odlyzko, Bounds for discriminants and related estimates for class numbers, regulators, and zeros of zeta functions: A survey of recent results, Sém. de Théorie des Nombres Bordeaux (Série 2) 2 (1990), 119–141.

    Article  MathSciNet  MATH  Google Scholar 

  101. M. Olivier, The computation of sextic fields with a cubic subfield and no quadratic subfield, Math. Comp. 58 (1992), 419–432.

    Article  MathSciNet  MATH  Google Scholar 

  102. M. Olivier, Corps sextiques primitifs, Ann. Inst. Fourier 40 (1990), 757–767.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  104. M. Pohst and H. Zassenhaus, Algorithmic algebraic number theory (3rd ed.), Cambridge Univ. Press, Cambridge (1993).

    Google Scholar 

  105. R. Quême, A computer algorithm for finding new Euclidean number fields, J. Théorie des Nombres Bordeaux 10 (1998), 33–48.

    Article  MATH  Google Scholar 

  106. D. Roberts, Density of cubic field discriminants, preprint.

    Google Scholar 

  107. X.-F. Roblot, Algorithmes de factorisation dans les extensions relatives et applications de la conjecture de Stark à la construction des corps de classes de rayon, Thesis, Université Bordeaux I (1997).

    Google Scholar 

  108. X.-F. Roblot, Unités de Stark et corps de classes de Hilbert, C. R. Acad. Sci. Paris 323 (1996), 1165–1168.

    MathSciNet  MATH  Google Scholar 

  109. X.-F. Roblot, Stark’s Conjectures and Hilbert’s Twelfth Problem, Experiment. Math., to appear.

    Google Scholar 

  110. R. Schertz, Zur expliciten Berechnung von Ganzheitbasen in Strahlklassenkörpern über einem imaginär-quadratischen Zahlkörper, J. Number Theory 34 (1990), 41–53.

    Article  MathSciNet  MATH  Google Scholar 

  111. R. Schertz, Galoismodulstruktur und elliptische Funktionen, J. Number Theory 39 (1991), 285–326.

    Article  MathSciNet  MATH  Google Scholar 

  112. R. Schertz, Problèmes de Construction en Multiplication Complexe, Sém. de Théorie des Nombres Bordeaux (Série 2), 4 (1992), 239–262.

    Article  MathSciNet  MATH  Google Scholar 

  113. R. Schertz, Construction of ray class fields by elliptic units, J. Théorie des Nombres Bordeaux 9 (1997), 383–394.

    Article  MathSciNet  MATH  Google Scholar 

  114. R. Schertz, Lower powers of elliptic units, preprint (1998).

    Google Scholar 

  115. A. Schwarz, M. Pohst, and F. Diaz y Diaz, A table of quintic number fields, Math. Comp. 63 (1994), 361–376.

    Article  MathSciNet  MATH  Google Scholar 

  116. J.-P. Serre, Corps locaux (2nd ed.), Hermann, Paris (1968). English translation: Graduate Texts in Math. 67, Springer-Verlag (1979).

    Google Scholar 

  117. G. Shimura, Abelian varieties with complex multiplication and modular functions, Princeton Univ. Press, Princeton, NJ (1998).

    MATH  Google Scholar 

  118. T. Shintani, On zeta-functions associated with the vector space of quadratic forms, J. Fac. Sci. Univ. Tokyo, Sec. 1a, 22 (1975), 25–66.

    MathSciNet  MATH  Google Scholar 

  119. C.-L. Siegel, The trace of totally positive and real algebraic integers, Ann. of Math. 46 (1945), 302–312.

    Article  MathSciNet  MATH  Google Scholar 

  120. J. Silverman, The arithmetic of elliptic curves, Graduate Texts in Math. 106, Springer-Verlag (1986).

    Google Scholar 

  121. J. Silverman, Advanced Topics in the arithmetic of elliptic curves, Graduate Texts in Math. 151, Springer-Verlag (1994).

    Google Scholar 

  122. D. Simon, Solving relative norm equations in number fields using S-units, Math. Comp., submitted.

    Google Scholar 

  123. D. Simon, Construction de polynômes de petit discriminant, C. R. Acad. Sci. Paris, to appear.

    Google Scholar 

  124. D. Simon, Equations dans les corps de nombres et discriminants minimaux, Thesis, Université Bordeaux I (1998).

    Google Scholar 

  125. C. Smyth, Totally positive algebraic integers of small trace, Ann. Inst. Fourier 33 (1984), 1–28.

    Article  MathSciNet  Google Scholar 

  126. C. Smyth, The mean value of totally real algebraic integers, Math. Comp. 42 (1984), 663–681.

    Article  MathSciNet  MATH  Google Scholar 

  127. C. Smyth, An inequality for polynomials, Proceedings of the CTNA Ottawa conference, to appear.

    Google Scholar 

  128. H. Suzuki, A generalization of Hilbert’s Theorem 94, Nagoya Math. J. 121 (1991), 161–169.

    MathSciNet  MATH  Google Scholar 

  129. J. Täte, Les conjectures de Stark sur les fonctions L d’Artin en s = 0, Progress in Math. 47, Birkhaüser, Boston (1984).

    Google Scholar 

  130. E. Tollis, Zeros of Dedekind zeta functions in the critical strip, Math. Comp. 66 (1997), 1295–1321.

    MathSciNet  MATH  Google Scholar 

  131. P. Walker, Elliptic functions, a constructive approach, John Wiley and Sons, New York (1996).

    MATH  Google Scholar 

  132. D. Wright, Distribution of discriminants of Abelian extensions, Proc. London Math. Soc. 58 (1989), 17–50.

    Article  MathSciNet  MATH  Google Scholar 

  133. D. Wright, personal communication.

    Google Scholar 

  134. D. Wright and A. Yukie, Prehomogeneous vector spaces and field extensions, Invent. math. 110 (1992), 283–314.

    Article  MathSciNet  MATH  Google Scholar 

  135. K. Yamamura, Maximal unramified extensions of imaginary quadratic number fields of small conductors, J. Théorie des nombres Bordeaux 9 (1997), 405–448.

    Article  MathSciNet  MATH  Google Scholar 

  136. H. Zantema, Class numbers and units, Computational methods in number theory II (H. W. Lenstra and R. Tijdeman, eds.), Math. Centrum tracts 155 (1982), 213–234.

    Google Scholar 

  137. H. Zimmer, Computational Problems, Methods, and Results in Algebraic Number Theory, Lecture Notes in Math. 262, Springer-Verlag (1972).

    Google Scholar 

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Cohen, H. (2000). Appendix C: Tables. In: Advanced Topics in Computational Number Theory. Graduate Texts in Mathematics, vol 193. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8489-0_12

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