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1992 | 62 | 2 | 173-206
Tytuł artykułu

Chebotarev formations and quantitative aspects of non-unique factorizations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
62
Numer
2
Strony
173-206
Opis fizyczny
Daty
wydano
1992
otrzymano
1992-01-27
poprawiono
1992-03-16
Twórcy
  • Institut für Mathematik, Karl-Franzens-Universität, Heinrichstrasse 36/IV, A-8010 Graz, Österreich
Bibliografia
  • [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.
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Bibliografia
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