Chebotarev formations and quantitative aspects of non-unique factorizations
Franz Halter-Koch
Acta Arithmetica, Tome 62 (1992), p. 173-206 / Harvested from The Polish Digital Mathematics Library
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Publié le : 1992-01-01
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     author = {Franz Halter-Koch},
     title = {Chebotarev formations and quantitative aspects of non-unique factorizations},
     journal = {Acta Arithmetica},
     volume = {62},
     year = {1992},
     pages = {173-206},
     zbl = {0762.11041},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav62i2p173bwm}
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Franz Halter-Koch. Chebotarev formations and quantitative aspects of non-unique factorizations. Acta Arithmetica, Tome 62 (1992) pp. 173-206. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav62i2p173bwm/

[000] [1] H. Delange, Généralisation du théorème de Ikehara, Ann. Sci. École Norm. Sup. 71 (1954), 213-242. | Zbl 0056.33101

[001] [2] E. Fogels, Zur Arithmetik quadratischer Zahlenkörper, Wiss. Abh. Univ. Riga, Kl. Math. Abt. 1 (1943), 23-47.

[002] [3] F. D. Fried and M. Jarden, Field Arithmetic, Springer, 1986.

[003] [4] A. Geroldinger, Über nicht-eindeutige Zerlegungen in irreduzible Elemente, Math. Z. 197 (1988), 505-529.

[004] [5] A. Geroldinger, Ein quantitatives Resultat über Faktorisierungen verschiedener Länge in algebraischen Zahlkörpern, Math. Z. 205 (1990), 159-162. | Zbl 0721.11041

[005] [6] A. Geroldinger, Arithmetical characterizations of divisor class groups, Arch. Math. (Basel) 54 (1990), 455-464. | Zbl 0703.20059

[006] [7] A. Geroldinger, Factorization of natural numbers in algebraic number fields, Acta Arith. 57 (1991), 365-373. | Zbl 0729.11054

[007] [8] A. Geroldinger, Arithmetical characterizations of divisor class groups, II, to appear. | Zbl 0830.20084

[008] [9] A. Geroldinger and F. Halter-Koch, Non-unique factorizations in block semigroups and arithmetical applications, Math. Slovaca, to appear. | Zbl 0765.11045

[009] [10] A. Geroldinger and J. Kaczorowski, Analytic and arithmetic theory of semigroups with divisor theory, to appear. | Zbl 0780.11046

[010] [11] F. Halter-Koch, Halbgruppen mit Divisorentheorie, Exposition. Math. 8 (1990), 27-66. | Zbl 0698.20054

[011] [12] F. Halter-Koch, A note on ray class fields of global fields, Nagoya Math. J. 120 (1990), 61-66. | Zbl 0721.11051

[012] [13] F. Halter-Koch, Finiteness theorems for factorizations, Semigroup Forum 44 (1992), 112-117. | Zbl 0751.20046

[013] [14] F. Halter-Koch, Typenhalbgruppen und Faktorisierungsprobleme, to appear.

[014] [15] F. Halter-Koch, A generalization of Davenport's constant and its arithmetical applications, Colloq. Math. 63 (1992), to appear. | Zbl 0760.11031

[015] [16] F. Halter-Koch, Factorization problems in formations of class number two, to appear. | Zbl 0816.11053

[016] [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. | Zbl 0736.11064

[017] [18] H. Hasse, Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, Teil I, Ia und II, Physica-Verlag, 1965.

[018] [19] N. Jacobson, Basic Algebra I, W. H. Freeman & Co., 1985.

[019] [20] J. Kaczorowski, Completely irreducible numbers in algebraic number fields, Funct. Approx. 11 (1981), 95-104. | Zbl 0476.12002

[020] [21] J. Kaczorowski, Some remarks on factorization in algebraic number fields, Acta Arith. 43 (1983), 53-68. | Zbl 0526.12006

[021] [22] J. Knopfmacher, Abstract Analytic Number Theory, North-Holland, 1975. | Zbl 0322.10001

[022] [23] H. W. Leopoldt, Zur Geschlechtertheorie in abelschen Zahlkörpern, Math. Nachr. 9 (1953), 350-362. | Zbl 0053.35502

[023] [24] W. Narkiewicz, On natural numbers having unique factorization in a quadratic number field, Acta Arith. 12 (1966), 1-22. | Zbl 0147.31001

[024] [25] W. Narkiewicz, Factorization of natural numbers in some quadratic number fields, Colloq. Math. 16 (1967), 257-268. | Zbl 0163.05002

[025] [26] W. Narkiewicz, On natural numbers having unique factorization in a quadratic number field, II, Acta Arith. 13 (1967), 123-129. | Zbl 0159.07202

[026] [27] W. Narkiewicz, A note on factorizations in quadratic fields, Acta Arith. 15 (1968), 19-22. | Zbl 0179.07703

[027] [28] W. Narkiewicz, Numbers with unique factorization in an algebraic number field, Acta Arith. 21 (1972), 313-322. | Zbl 0215.07301

[028] [29] W. Narkiewicz, Finite abelian groups and factorization problems, Colloq. Math. 42 (1979), 319-330. | Zbl 0514.12004

[029] [30] W. Narkiewicz, Numbers with all factorizations of the same length in a quadratic number field, Colloq. Math. 45 (1981), 71-74. | Zbl 0486.12003

[030] [31] W. Narkiewicz, Number Theory, World Scientific, 1983.

[031] [32] W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, Springer, 1990. | Zbl 0717.11045

[032] [33] W. Narkiewicz and J. Śliwa, Finite abelian groups and factorization problems , II, Colloq. Math. 46 (1982), 115-122. | Zbl 1164.20358

[033] [34] R. W. K. Odoni, On a problem of Narkiewicz, J. Reine Angew. Math. 288 (1976), 160-167. | Zbl 0335.12019

[034] [35] P. Rémond, Étude asymptotique de certaines partitions dans certains semi-groupes, Ann. Sci. École Norm. Sup. 83 (1966), 343-410. | Zbl 0157.09602

[035] [36] J. P. Serre, Zeta and L functions, in: Arithmetical Algebraic Geometry, Harper and Row, 1965, 82-92.

[036] [37] J. Śliwa, A note on factorizations in algebraic number fields, Bull. Acad. Polon. Sci. 24 (1976), 313-314. | Zbl 0334.12015

[037] [38] J. Śliwa, Factorizations of distinct lengths in algebraic number fields, Acta Arith. 31 (1976), 399-417. | Zbl 0347.12005

[038] [39] E. Weiss, Algebraic Number Theory, McGraw-Hill, 1963. | Zbl 0115.03601