Schappacher, NorbertOverview
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Most widely held works by
Norbert Schappacher
The shaping of arithmetic after C.F. Gauss's Disquisitiones Arithmeticae
by Catherine Goldstein
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14 editions published between 2006 and 2011 in English and held by 525 WorldCat member libraries worldwide The cultural historian, Theodore Merz called it the great book with seven seals, the mathematician Leopold Kronecker, "the book of all books": already one century after their publication, C.F. Gauss's "Disquisitiones Arithmeticae" (1801) had acquired an almost mythical reputation. It had served throughout the XIXth century and beyond as an ideal of exposition in matters of notation, problems and methods; as a model of organisation and theory building; and of course as a source of mathematical inspiration. Various readings of the "Disquisitiones Arithmeticae" have left their mark on developments as different as Galois's theory of algebraic equations, Lucas's primality tests, and Dedekind's theory of ideals. The present volume revisits successive periods in the reception of the Disquisitiones: it studies which parts were taken up and when, which themes were further explored. It also focuses on how specific mathematicians reacted to Gauss's book: Dirichlet and Hermite, Kummer and Genocchi, Dedekind and Zolotarev, Dickson and Emmy Noether, among others. An astounding variety of research programmes in the theory of numbers can be traced back to it.; The 19 authors  mathematicians, historians, philosophers  who have collaborated on this volume contribute indepth studies on the various aspects of the bicentennial voyage of this mathematical text through history, and the way that the number theory we know today came into being
Periods of Hecke characters
by Norbert Schappacher
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16 editions published between 1986 and 1988 in English and German and held by 457 WorldCat member libraries worldwide The starting point of this Lecture Notes volume is Deligne's theorem about absolute Hodge cycles on abelian varieties. Its applications to the theory of motives with complex multiplication are systematically reviewed. In particular, algebraic relations between values of the gamma function, the socalled formula of Chowla and Selberg and its generalization and Shimura's monomial relations among periods of CM abelian varieties are all presented in a unified way, namely as the analytic reflections of arithmetic identities beetween Hecke characters, with gamma values corresponding to Jacobi sums. The last chapter contains a special case in which Deligne's theorem does not apply
Regulators in analysis, geometry, and number theory
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10 editions published between 1999 and 2000 in English and held by 234 WorldCat member libraries worldwide "The focus in this book is on the theory of regulators and secondary invariants, with articles written and refereed by experts in their respective fields
Les conjectures de Stark sur les fonctions L d'Artin en s=O : notes d'un cours à Orsay [de] John Tate
by John Torrence Tate
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11 editions published in 1984 in French and English and held by 228 WorldCat member libraries worldwide
Beilinson's conjectures on special values of Lfunctions
by Oberwolfach conference
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10 editions published in 1988 in English and Undetermined and held by 221 WorldCat member libraries worldwide
Algebraic number theory
by Jürgen Neukirch
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5 editions published in 1999 in English and held by 71 WorldCat member libraries worldwide "The present book has as its aim to resolve a discrepancy in the textbook literature and ... to provide a comprehensive introduction to algebraic number theory which is largely based on the modern, unifying conception of (onedimensional) arithmetic algebraic geometry. ... Despite this exacting program, the book remains an introduction to algebraic number theory for the beginner ... The author discusses the classical concepts from the viewpoint of Arakelov theory ... The treatment of class field theory is ... particularly rich in illustrating complements, hints for further study, and concrete examples ... The concluding chapter VII on zetafunctions and Lseries is another outstanding advantage of the present textbook ... The book is, without any doubt, the most uptodate, systematic, and theoretically comprehensive textbook on algebraic number field theory available." W. Kleinert in Z.blatt f. Math., 1992 "The author's enthusiasm for this topic is rarely as evident for the reader as in this book.  A good book, a beautiful book." F. Lorenz in Jber. DMV 1995 "The present work is written in a very careful and masterly fashion. It does not show the pains that it must have caused even an expert like Neukirch. It undoubtedly is liable to become a classic; the more so as recent developments have been taken into account which will not be outdated quickly. Not only must it be missing from the library of no number theorist, but it can simply be recommended to every mathematician who wants to get an idea of modern arithmetic." J. Schoissengeier in Montatshefte Mathematik 1994
Eine diophantische Invariante von Singularitäten über nichtarchimedischen Körpern
by Norbert Schappacher
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4 editions published in 1978 in German and Undetermined and held by 22 WorldCat member libraries worldwide
Disquisitiones arithmeticae
by Carl Friedrich Gauss
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6 editions published in 2006 in Latin and German and held by 17 WorldCat member libraries worldwide
Politisches in der Mathematik  Versuch einer Spurensicherung
by Norbert Schappacher
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4 editions published in 2002 in German and held by 16 WorldCat member libraries worldwide
Ktheory : Strasbourg, 1992
by Colloque international de KThéorie
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1 edition published in 1994 in English and held by 16 WorldCat member libraries worldwide
Mathematics in Berlin
by Heinrich Begehr
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1 edition published in 1998 in English and held by 6 WorldCat member libraries worldwide This book is a font of information for readers interested in the mathematical past and present of Berlin. It presents a comprehensive, condensed overview of mathematical activity in Berlin, beginning with the foundation of the Academy by Leibniz and carrying over almost to the present day. Many towering figures in mathematical history worked in Berlin, and thus most of the chapters of this book are essentially concise biographies of these luminaries. The presentations are held together and complemented by a few articles examining the overall development of entire periods of scientific life at Berlin. Chapters cover the foundation of the University of Berlin, the "Golden Age" of mathematics (spanning the second half of the 19th century), the Nazi period, the development of mathematics in East and West Berlin during the political division of the city, and the merging of the formerly separated mathematical communities with the reunification of Germany
The theory of algebraic number fields
by David Hilbert
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3 editions published in 1998 in English and held by 6 WorldCat member libraries worldwide This book is an English translation of Hilbert's Zahlbericht, the monumental report on the theory of algebraic number field which he composed for the German Mathematical Society. In this magisterial work Hilbert provides a unified account of the development of algebraic number theory up to the end of the nineteenth century. He greatly simplified Kummer's theory and laid the foundation for a general theory of abelian fields and class field theory. David Hilbert (18621943) made great contributions to many areas of mathematics  invariant theory, algebraic number theory, the foundations of geometry, integral equations, the foundations of mathematics and mathematical physics. He is remembered also for his lecture at the Paris International Congress of Mathematicians in 1900 where he presented a set of 23 problems "from the discussion of which an advancement of science may be expected"His expectations have been amply fulfilled
REDUCTION DE FAMILLES DE POINTS CM
by Christophe Cornut
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2 editions published in 2000 in French and held by 2 WorldCat member libraries worldwide UNE COURBE ELLIPTIQUE MODULAIRE EST EQUIPPEE D'UNE FAMILLE DE POINTS CM SPECIAUX, LES POINTS DE HEEGNER, QUI SONT DEFINIS SUR DES EXTENSIONS DIHEDRALES DU CORPS DES RATIONNELS. NOUS DEMONTRONS UNE CONJECTURE DE BARRY MAZUR (ICM 83), SELON LAQUELLE LES POINTS DE HEEGNER DONT LE CONDUCTEUR DECRIT LES PUISSANCES D'UN NOMBRE PREMIER P FIXE DONNENT NAISSANCE A DES POINTS DE RANG INFINI DANS LES GROUPES DE MORDELLWEIL DE LA COURBE ELLIPTIQUE LE LONG DE LA PEXTENSION ANTICYCLOTOMIQUE DU CORPS DE MULTIPLICATION COMPLEXE. NOUS ETUDIONS POUR CELA PLUS GENERALEMENT LES PROPRIETES DE SURJECTIVITE DE LA REDUCTION SUPERSINGULIERE SIMULTANEE DE FAMILLES DE POINTS CM
Weiterentwicklung oder Umbruch? : zu Oscar Zariskis Arithmetisierung der algebraischen Geometrie = Continuité ou rupture? : à propos de l'arithmétisation de la géometrie algébrique selon Oscar Zariski
by Silke Slembek
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2 editions published in 2002 in German and held by 2 WorldCat member libraries worldwide
Quelques courants majeurs dans le développement de la multiplication complexe
by J.M Lemaire
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2 editions published between 1996 and 2008 in French and held by 2 WorldCat member libraries worldwide Du 6 au 8 janvier 1996, le Laboratoire Jean Dieudonné (CNRS et Université de Nice, Sophia Antipolis) a organisé un colloque à la mémoire de Jean Dieudonné avec le concours de l'Académie des sciences et de l'I.H.E.S. Il s'agit ici de la conférence filmée de Norbert Schappacher. Le 12ème problème de Hilbert propose une façon conjecturale d'engendrer les extensions abéliennes d'un corps de nombres (en généralisant le théorème dit de Kronecker et Weber suivant lequel les extensions abéliennes de Q sont engendrées par des racines de l'unité) ainsi que les extensions des corps quadratiques imaginaires (engendrées par des valeurs de fonctions modulaires et elliptiques liées aux courbes elliptiques à multiplication complexe). En fait, dans le cas du corps quadratique imaginaire, la formulation de Hilbert était incorrecte. Cette erreur, qui n'a été découverte que 14 ans plus tard, est discutée à la fois du point de vue historique (l'autorité de Hilbert...) et mathématique. L'exposé présente ensuite des énoncés analogues en dimension supérieure et évoque les développements récents (motifs, points de Heegner)
Rational points : Seminar Bonn/Wuppertal 1983/84
by Gerd Faltings
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1 edition published in 1986 in English and held by 2 WorldCat member libraries worldwide
On the second Kgroup of an elliptic curve
by Klaus Rolshausen
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2 editions published in 1997 in English and held by 2 WorldCat member libraries worldwide
Développement de la loi de groupe sur une cubique
by Norbert Schappacher
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1 edition published in 1990 in German and held by 1 WorldCat member library worldwide
Das Mathematische Institut der Universität Göttingen 19291950
by Norbert Schappacher
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1 edition published in 1998 in German and held by 1 WorldCat member library worldwide
Séries de Kronecker et fonctions L des puissances symétriques de courbes elleptiques sur Q
by JeanFrançois Mestre
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1 edition published in 1989 in German and held by 1 WorldCat member library worldwide more
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Associated Subjects
Algebra Algebraic fields Algebraic number theory Beilinson's conjectures Cyclotomy Forms, Modular Geometry Geometry, Algebraic Germany GermanyBerlin Hecke operators Ktheory Lfunctions Mathematicians Mathematics MathematicsStudy and teaching (Higher) Multiplication, Complex Number theory Rational points (Geometry) Regulators (Mathematics) Series, Taylor's Stark's conjectures

Alternative Names
Schappacher, N.
Schappacher, N. (Norbert)
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