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The Totally Real Primitive Number Fields of Discriminant at Most 109

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Book cover Algorithmic Number Theory (ANTS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 4076))

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Abstract

In this note we report on the enumeration of totally real number fields of discriminant at most 109 with no proper subfield and give some statistics on their properties.

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References

  1. Belabas, K.: A fast algorithm to compute cubic fields. Math. Comp. 66, 1213–1237 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  2. Belabas, K.: Paramétrisation de structures algébriques et densité de discriminants [d’après M. Bhargava]. Astérisque 299, 267–299 (2005)

    MathSciNet  Google Scholar 

  3. Bhargava, M.: The density of discriminants of quartic rings and fields. Ann. of Math. 162, 1031–1063 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cohen, H.: A course in computational algebraic number theory. Springer, Berlin (1993)

    MATH  Google Scholar 

  5. Cohen, H.: Counting A 4 and S 4 number fields with given resolvent cubic. In: Fields Inst. Commun., vol. 41, pp. 159–168. Amer. Math. Soc., Providence, RI (2004)

    Google Scholar 

  6. Cohen, H., Diaz y Diaz, F., Olivier, M.: A survey of discriminant counting. In: Fieker, C., Kohel, D.R. (eds.) ANTS 2002. LNCS, vol. 2369, pp. 80–94. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  7. Cohen, H., Diaz y Diaz, F., Olivier, M.: Counting discriminants of number fields. J. Th. Nombres Bordeaux (to appear)

    Google Scholar 

  8. Cohen, H., Martinet, J.: Class groups of number fields: numerical heuristics. Math. Comp. 48, 123–137 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  9. Daberkow, M., Fieker, C., Klüners, J., Pohst, M., Roegner, K., Wildanger, K.: KANT V4. J. Symbolic Comp. 24, 267–283 (1997)

    Article  MATH  Google Scholar 

  10. Ford, D., Pohst, M.: The totally real A 5 extension of degree 6 with minimum discriminant. Experiment. Math. 1, 231–235 (1992)

    MATH  MathSciNet  Google Scholar 

  11. Klüners, J.: The number of S 4-fields with given discriminant. Acta Arithmetica (to appear)

    Google Scholar 

  12. Klüners, J., Malle, G.: A database for field extensions of the rationals. LMS J. Comput. Math. 4, 182–196 (2001)

    MATH  MathSciNet  Google Scholar 

  13. Malle, G.: On the distribution of Galois groups. J. Number Theory 92, 315–329 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Malle, G.: On the distribution of Galois groups. II. Experiment. Math. 13, 129–135 (2004)

    MATH  MathSciNet  Google Scholar 

  15. Takeuchi, K.: Totally real algebraic number fields of degree 9 with small discriminant. Saitama Math. J. 17, 63–85 (1999)

    MATH  MathSciNet  Google Scholar 

  16. Washington, L.C.: Introduction to cyclotomic fields, 2nd edn. Graduate Texts in Mathematics, vol. 83. Springer, New York (1997)

    MATH  Google Scholar 

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Malle, G. (2006). The Totally Real Primitive Number Fields of Discriminant at Most 109 . In: Hess, F., Pauli, S., Pohst, M. (eds) Algorithmic Number Theory. ANTS 2006. Lecture Notes in Computer Science, vol 4076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11792086_9

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  • DOI: https://doi.org/10.1007/11792086_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36075-9

  • Online ISBN: 978-3-540-36076-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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