ArticleOriginal scientific text

Title

Chebotarev formations and quantitative aspects of non-unique factorizations

Authors 1

Affiliations

  1. Institut für Mathematik, Karl-Franzens-Universität, Heinrichstrasse 36/IV, A-8010 Graz, Österreich

Bibliography

  1. H. Delange, Généralisation du théorème de Ikehara, Ann. Sci. École Norm. Sup. 71 (1954), 213-242.
  2. E. Fogels, Zur Arithmetik quadratischer Zahlenkörper, Wiss. Abh. Univ. Riga, Kl. Math. Abt. 1 (1943), 23-47.
  3. F. D. Fried and M. Jarden, Field Arithmetic, Springer, 1986.
  4. A. Geroldinger, Über nicht-eindeutige Zerlegungen in irreduzible Elemente, Math. Z. 197 (1988), 505-529.
  5. A. Geroldinger, Ein quantitatives Resultat über Faktorisierungen verschiedener Länge in algebraischen Zahlkörpern, Math. Z. 205 (1990), 159-162.
  6. A. Geroldinger, Arithmetical characterizations of divisor class groups, Arch. Math. (Basel) 54 (1990), 455-464.
  7. A. Geroldinger, Factorization of natural numbers in algebraic number fields, Acta Arith. 57 (1991), 365-373.
  8. A. Geroldinger, Arithmetical characterizations of divisor class groups, II, to appear.
  9. A. Geroldinger and F. Halter-Koch, Non-unique factorizations in block semigroups and arithmetical applications, Math. Slovaca, to appear.
  10. A. Geroldinger and J. Kaczorowski, Analytic and arithmetic theory of semigroups with divisor theory, to appear.
  11. F. Halter-Koch, Halbgruppen mit Divisorentheorie, Exposition. Math. 8 (1990), 27-66.
  12. F. Halter-Koch, A note on ray class fields of global fields, Nagoya Math. J. 120 (1990), 61-66.
  13. F. Halter-Koch, Finiteness theorems for factorizations, Semigroup Forum 44 (1992), 112-117.
  14. F. Halter-Koch, Typenhalbgruppen und Faktorisierungsprobleme, to appear.
  15. F. Halter-Koch, A generalization of Davenport's constant and its arithmetical applications, Colloq. Math. 63 (1992), to appear.
  16. F. Halter-Koch, Factorization problems in formations of class number two, to appear.
  17. F. Halter-Koch and W. Müller, Quantitative aspects of non-unique factorization : A general theory with applications to algebraic function fields, J. Reine Angew. Math. 421 (1991), 159-188.
  18. H. Hasse, Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, Teil I, Ia und II, Physica-Verlag, 1965.
  19. N. Jacobson, Basic Algebra I, W. H. Freeman & Co., 1985.
  20. J. Kaczorowski, Completely irreducible numbers in algebraic number fields, Funct. Approx. 11 (1981), 95-104.
  21. J. Kaczorowski, Some remarks on factorization in algebraic number fields, Acta Arith. 43 (1983), 53-68.
  22. J. Knopfmacher, Abstract Analytic Number Theory, North-Holland, 1975.
  23. H. W. Leopoldt, Zur Geschlechtertheorie in abelschen Zahlkörpern, Math. Nachr. 9 (1953), 350-362.
  24. W. Narkiewicz, On natural numbers having unique factorization in a quadratic number field, Acta Arith. 12 (1966), 1-22.
  25. W. Narkiewicz, Factorization of natural numbers in some quadratic number fields, Colloq. Math. 16 (1967), 257-268.
  26. W. Narkiewicz, On natural numbers having unique factorization in a quadratic number field, II, Acta Arith. 13 (1967), 123-129.
  27. W. Narkiewicz, A note on factorizations in quadratic fields, Acta Arith. 15 (1968), 19-22.
  28. W. Narkiewicz, Numbers with unique factorization in an algebraic number field, Acta Arith. 21 (1972), 313-322.
  29. W. Narkiewicz, Finite abelian groups and factorization problems, Colloq. Math. 42 (1979), 319-330.
  30. W. Narkiewicz, Numbers with all factorizations of the same length in a quadratic number field, Colloq. Math. 45 (1981), 71-74.
  31. W. Narkiewicz, Number Theory, World Scientific, 1983.
  32. W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, Springer, 1990.
  33. W. Narkiewicz and J. Śliwa, Finite abelian groups and factorization problems , II, Colloq. Math. 46 (1982), 115-122.
  34. R. W. K. Odoni, On a problem of Narkiewicz, J. Reine Angew. Math. 288 (1976), 160-167.
  35. P. Rémond, Étude asymptotique de certaines partitions dans certains semi-groupes, Ann. Sci. École Norm. Sup. 83 (1966), 343-410.
  36. J. P. Serre, Zeta and L functions, in: Arithmetical Algebraic Geometry, Harper and Row, 1965, 82-92.
  37. J. Śliwa, A note on factorizations in algebraic number fields, Bull. Acad. Polon. Sci. 24 (1976), 313-314.
  38. J. Śliwa, Factorizations of distinct lengths in algebraic number fields, Acta Arith. 31 (1976), 399-417.
  39. E. Weiss, Algebraic Number Theory, McGraw-Hill, 1963.
Pages:
173-206
Main language of publication
English
Received
1992-01-27
Accepted
1992-03-16
Published
1992
Exact and natural sciences