4637 Allan Adler: Magic cubes and the 3-adic zeta function. Math. Intell. 14/3 (1992), 14-23. 1755 P. Alexandrov (ed.): Die Hilbertschen Probleme. Leipzig 1983. 11528 Emil Artin: Quadratische Ko''rper im Gebiete der ho''heren Kongruenzen I. Dissertation. In Emil Artin's Collected Papers, 1-... M. Bertin a.o.: Pisot and Salem numbers. Birkhuser 1992, 290p. 3-7643-2648-4. SFR 158. J.W.S. Cassels: Local fields. Cambridge UP 1986. 1752 J.W.S. Cassels/A. Froehlich (ed.): Algebraic number theory. Academic Press 1967. The standard reference for higher algebraic number theory. 2790 S. Chatterji/Ulrich Kulisch/Detlef Laugwitz/Roman Liedl/Walter Purkert (ed.): Jahrbuch Ueberblicke Mathematik 1991. Vieweg 1991. 2069 Harvey Cohn: Advanced number theory. Dover 1980. M. Coleman: The distribution of points at which norm-forms are prime. J. Number theory 41 (1992), 359-378. New results on the multidimensional distribution of prime ideals in number fields. E. Dade/O. Taussky/Hans Zassenhaus: On the theory of orders, in particular on the semigroup of ideal classes and genera of an order in an algebraic number field. Math. Ann. 148 (1962), 31-64. Richard Dedekind: Theory of algebraic integers. Cambridge UP 1996, 160p. 0-521-56518-9. Pds. 15. With an introduction to number theory by John Stillwell. 1959 Max Deuring: Die Klassenkoerper der komplexen Multiplikation. Enzykl. der math. Wiss. I/2/Heft 10,2. Harold Edwards: Divisor theory. Birkhaeuser 1990, 180p. DM 68. Some new concepts for algebraic number theory. The reviewer seems not very convinced. 1772 Otto Endler: Valuation theory. Springer 1972. 1898 Philipp Furtwaengler: Allgemeine Theorie der algebraischen Zahlen. Enz. math. Wiss. 1/2/Heft 8,2. 1988 Carl Friedrich Gauss: Disquisitiones arithmeticae. (Werke, erster Band). Olms 1981. ISBN 3-487-04633-4. Kurt Girstmair: Character coordinates and annihilators of cyclotomic numbers. Manuscripta Math. 59 (1987), 375-389. Kurt Girstmair: Ein von-Staudt-Clausenscher Satz fuer periodische Bernoullizahlen. Monatshefte Math. 104 (1987), 109-118. Kurt Girstmair: An index formula for the relative class number of an abelian number field. J. Number theory 32 (1989), 100-110. Kurt Girstmair: Dirichlet convolution of cotangent numbers and relative class number formulas. Monathefte Math. 110 (1990), 231-256. 4993 Kurt Girstmair: Klassenzahlformeln fuer Kreisteilungskoerper. 2790 Chatterji/, 3-22. Kurt Girstmair: On the cosets of the 2q-power group in the unit gorup modulo p. Abh. Math. Sem. Hamburg 62 (1992), 217-232. Kurt Girstmair: On the branch order of the ring of integers of an abelian number field. Acta Arithm. 62 (1992), 297-301. Kurt Girstmair: On the trace of the ring of integers of an abelian number field. Acta Arithm. 62 (1992), 383-389. 5759 Kurt Girstmair: The relative class numbers of imaginary cyclic fields of degrees 4,6,8, and 10. Mathematics of Comp. 61 (1993), 881-887. Kurt Girstmair: Eine Verbindung zwischen den arithmetischen Eigenschaften verallgemeinerter Bernoullizahlen. Expos. Math. 11 (1993), 47-63. Kurt Girstmair: The digits of 1/p in connection with class number factors. Acta Arithm. 67 (1994), 381-386. Helmut Hasse: Bericht ueber neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkoerper. Jber. DMV 35 (1926), ..., 36 (1927), ..., 39 (1930), ... 1787 Helmut Hasse: Zahlentheorie. Akademie-Verlag 1949. Esistono edizioni piu' nuove, con molte aggiunte. 3574 Helmut Hasse: Ueber die Klassenzahl abelscher Zahlkoerper. Springer 1985. 1878 Michiel Hazewinkel: Review of the books "Class field theory" by Neukirch and "Local class field theory" by Iwasawa. Bull. AMS 21 (1989), 95-101. [3323] 1715 Erich Hecke: Vorlesungen ueber die Theorie der algebraischen Zahlen. Chelsea 1948. Erich Hecke: Ueber die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung. Math. Ann. 112 (1936), 664-669. Hans Arnold Heilbronn: On the class-number in imaginary quadratic fields. Quarterly J. Math. 5 (1934), 150-160. Hans-Arnold Heilbronn/E.H. Linfoot: On the imaginary quadratic corpora of class-number one. Quarterly J. Math. 5 (1934), 293-301. Heukers/H. Schlickewei: The equation x+y=1 in finitely generated groups. Acta Arithm. 78 (1996), 189-199. 4578 David Hilbert: Gesammelte Abhandlungen. Erster Band: Zahlentheorie. Chelsea. 3622 Makoto Ishida: The genus fields of algebraic number fields. SLN Math. 555. K. Iwasawa: A class number formula for cyclotomic fields. Annals Math. 76 (1962), 171-179. K. Iwasawa: Local class field theory. Oxford UP 1986, 155p. Pds. 35. 1714 Gerald Janusz: Algebraic number fields. Academic Press 1973. 8459 Giuseppe Jurman: Breve introduzione alla teoria dei numeri. Internet 1992, 16p. 1952 Helmut Koch: Galoissche Theorie der p-Erweiterungen. Springer 1970. 16016 Helmut Koch: Zahlentheorie. Algebraische Zahlen und Funktionen. Vieweg 1997, 340p. Eur 27. Helmut Koch: Algebraic numbers and functions. 2000. Tomio Kubota: Foundations of class field theory through properties of space figures. Sugaku 44 (1992), 1-12. Explains the recent direct proof of the reciprocity law for the n-th power residue symbol using geometry of numbers. Remarkable. See Zentralblatt 760 (1993), 46-47. 1884 G. Lachaud: On real quadratic fields. Bull. AMS 17 (1987), 307-311. [3323] 4591 Edmund Landau: Einfuehrung in die elementare und analytische Theorie der algebraischen Zahlen und Ideale. Teubner 1927. 1753 Serge Lang: Algebraic number theory. Springer 1986. 3475 Serge Lang: Cyclotomic fields. Both parts in one volume. Springer 1990. Andrew Lazarus: Gaussian periods and units in certain cyclic fields. Proc. AMS 115 (1992), 961-968. 7311 Franz Lemmermeyer: The euclidean algorithm in algebraic number fields. Internet, 31p. H. Leopoldt: Ueber Einheitengruppe und Klassenzahl reeller abelscher Zahlkoerper. Abh. Dt. Ak. Wiss. Berlin 1953/2. G. Lettl: Stickelberger elements and cotangent numbers. Preprint. 16017 Armin Leutbecher: Zahlentheorie. Springer 1996, 350p. Eur 25. Falko Lorenz: Einfuehrung in die Algebra. 2 volumes. Bibl. Inst. 1990, 700p. DM 82. Should be a very good introduction to Galois theory (volume 1) and to local class field theory (volume 2). Falko Lorenz: Algebraische Zahlentheorie. Bibl. Inst. 1993, 350p. 3-411-16701-7. DM 38. 2603 M.-P. Malliavin: Algebre commutative. Masson 1985. Very clear. Especially good as a foundation for algebraic number theory. 1736 Daniel Marcus: Number fields. Springer 1977. Akito Namura: On the class numbers of certain Hilbert class fields. Man. Math. 79 (1993), 379-390. 3545 Wladyslaw Narkiewicz: Elementary and analytic theory of algebraic numbers. Springer 1990. 1877 Juergen Neukirch: Klassenkoerpertheorie. Bibl. Inst. 1969. Juergen Neukirch: Neubegruendung der Klassenkoerpertheorie. Math. Zeitschr. 186 (1984), 557-574. 3575 Juergen Neukirch: Class field theory. Springer 1986. 4156 Juergen Neukirch: Algebraische Zahlentheorie. Springer 1992. Vladimir Platonov/Andrei Rapinchuk: Algebraic groups and number theory. 1993, 580p. Pds. 80. Harry Pollard/H. Diamond: The theory of algebraic numbers. Dover 1999. 0-486-404544. $8. Klaus Pommerening/N. Guthschmidt/P. Hafkus/W. Paus: Algebraische Zahlen und algebraische Funktionen. Seminarausarbeitung, Berlin 1968. 170p. Klaus Pommerening: Der euklidische Algorithmus. Alef 5 (1985), 31-70. Klaus Pommerening: Primzerlegung in imagina''r-quadratischen Zahlringen und Summen von zwei Quadraten. Alef 17 (1995), 43-64. Clifford Queen: A simple characterization of principal ideal domains. Acta Arithm. 64 (1993), 125-128. An integer domain is a PID iff it has a very natural and simple type of "norm". D. Ramakrishnan/R. Valenza: Fourier analysis on number fields. Springer 1999, 350p. DM 79. 1998 Paulo Ribenboim: Algebraic numbers. Wiley 1972. K. Roggenkamp/M. Taylor: Group rings and class groups. Birkhaeuser 1992, 216p. 3-7643-2734-0. DM 76. P. Samuel: Theorie algebrique des nombres. Hermann 1967. C. Schmidt: Groessencharaktere und Relativklassenzahl abelscher Zahlkoerper. J. Number theory 11 (1979), 128-159. C. Schmidt: Stickelbergerideale und Kreiseinheiten zu Klassenkoerpern abelscher Zahlkoerper. J. reine u. angew. Math. 353 (1984), 14-54. 3287 Joachim Schwermer: Ueber Reziprozitaetsgesetze in der Zahlentheorie. 2718 Knoerrer, 29-69. 7052 Jean-Pierre Serre: Local fields. Springer 1979. 3596 Jean-Pierre Serre: Cohomologie galoisienne. SLN Math. 5 (1986). Jean-Pierre Serre: Algebraic groups and class fields. Springer 1988, 210p. DM 72. B. Setzer: The determination of all imaginary, quartic, abelian number fields with class number 1. Math. Comp. 35 (1980), 1383-1386. 2733 Igor Shafarevich: Abelian and nonabelian mathematics. Math. Intell. 13/1 (1991), 67-75. Harold Shapiro/Gerson Sparer: Minimal bases for cubic fields. Commun. pure appl. Math. 44 (1991), 1121-1136. Goro Shimura: Class fields over real quadratic fields and Hecke operators. Annals Math. 95 (1972), 130-190. 1866 Ladislav Skula: Divisorentheorie einer Halbgruppe. Math. Zt. 114 (1970), 113-120. [3323] V. Snaith: Galois module structure. AMS 1994, 210p. $39. Harold Stark: The analytic theory of algebraic numbers. Springer 1993. 4806 Harold Stark: Galois theory, algebraic number theory, and zeta functions. 4740 Waldschmidt, 313-393. 1984 Harold Stark: A complete determination of the complex quadratic fields of class-number one. Michigan Math. J. 14 (1967), 1-27. [3323] 3621 Ian Stewart/David Tall: Algebraic number theory. Chapman and Hall 1987. Peter Swinnerton-Dyer: A brief guide to algebraic number theory. Cambridge UP 2001, 160p. Pds. 16 (pb.). Toshikazu Takagi: The cuspidal class number formula for the modular curves ... J. Algebra 158 (1993), 515-549. Francisco Thaine: On the relation between units and Jacobi sums in prime cyclotomic fields. Man. Math. 73 (1991), 127-151. 9791 Stefan Treatman: Euclidean systems. Dissertation, Univ. Michigan 1996. 9854 F. Vivaldi: Algebraic number theory and Hamiltonian chaos. In 4779 Luck/Moussa/Waldschmidt, 294-301. 4714 Lawrence Washington: Introduction to cyclotomic fields. Springer 1982. 1923 Andre' Weil: Basic number theory. Springer 1974. 1905 Andre' Weil: Adeles and algebraic groups. Birkhaeuser 1982. 1964 Edwin Weiss: Algebraic number theory. McGraw-Hill 1963. 1904 Hermann Weyl: Algebraische Zahlentheorie. Bibl. Inst. 1966. 3345 Gisbert Wuestholz: Diophantische Geometrie: Effektivitaet und einige Probleme. Jber. DMV 93 (1991), 147-160. Fei Xu/Jianqiang Zhao: Maximal independent systems of units in global function fields. Acta Arithm. 78 (1996), 1-10. 1942 Don Zagier: Zetafunktionen und quadratische Koerper. Springer 1981. | |
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