Schappacher, Norbert
Overview
Works:  31 works in 116 publications in 4 languages and 1,917 library holdings 

Genres:  Conference proceedings History Biography 
Roles:  Author, Editor, Translator, Author of introduction, Interviewee, Redactor 
Classifications:  QA241, 512 
Publication Timeline
.
Most widely held works by
Norbert Schappacher
The shaping of arithmetic after C.F. Gauss's Disquisitiones Arithmeticae
by
Catherine Goldstein(
)
16 editions published between 2006 and 2011 in English and held by 528 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
16 editions published between 2006 and 2011 in English and held by 528 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(
Book
)
16 editions published between 1986 and 1988 in English and German and held by 478 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
16 editions published between 1986 and 1988 in English and German and held by 478 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
by
Alexander Reznikov(
Book
)
11 editions published between 1999 and 2000 in English and held by 247 WorldCat member libraries worldwide
A short historical and mathematical overview of the theory of regulators from its number theoretic origins, and its connections to analysis, topology, differential geometry, and algebra, is presented by the editors in the introduction, with key topics noted as follows: hyperbolic volume and the Borel regulator, the ChernSimons invariant, the BlochBeilinson regulator, polylogarithms (classical and elliptic), and analytic torsion."Jacket
11 editions published between 1999 and 2000 in English and held by 247 WorldCat member libraries worldwide
A short historical and mathematical overview of the theory of regulators from its number theoretic origins, and its connections to analysis, topology, differential geometry, and algebra, is presented by the editors in the introduction, with key topics noted as follows: hyperbolic volume and the Borel regulator, the ChernSimons invariant, the BlochBeilinson regulator, polylogarithms (classical and elliptic), and analytic torsion."Jacket
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(
Book
)
11 editions published in 1984 in French and English and held by 241 WorldCat member libraries worldwide
11 editions published in 1984 in French and English and held by 241 WorldCat member libraries worldwide
Beilinson's conjectures on special values of Lfunctions
by
M Rapoport(
Book
)
10 editions published between 1988 and 2014 in English and Undetermined and held by 222 WorldCat member libraries worldwide
Beilinson's Conjectures on Special Values of LFunctions
10 editions published between 1988 and 2014 in English and Undetermined and held by 222 WorldCat member libraries worldwide
Beilinson's Conjectures on Special Values of LFunctions
Algebraic number theory
by
Jürgen Neukirch(
Book
)
5 editions published in 1999 in English and held by 75 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
5 editions published in 1999 in English and held by 75 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
Mathematics in Berlin
by
Heinrich G. W Begehr(
)
2 editions published in 1998 in English and held by 22 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
2 editions published in 1998 in English and held by 22 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
Eine diophantische Invariante von Singularitäten über nichtarchimedischen Körpern
by
Norbert Schappacher(
Book
)
4 editions published in 1978 in German and Undetermined and held by 22 WorldCat member libraries worldwide
4 editions published in 1978 in German and Undetermined and held by 22 WorldCat member libraries worldwide
Politisches in der Mathematik  Versuch einer Spurensicherung
by
Norbert Schappacher(
)
4 editions published in 2002 in German and held by 16 WorldCat member libraries worldwide
4 editions published in 2002 in German and held by 16 WorldCat member libraries worldwide
Disquisitiones arithmeticae
by
Carl Friedrich Gauss(
Book
)
6 editions published in 2006 in Latin and German and held by 16 WorldCat member libraries worldwide
6 editions published in 2006 in Latin and German and held by 16 WorldCat member libraries worldwide
Ktheory : Strasbourg, 1992
by Colloque international de Kthéorie(
Book
)
1 edition published in 1994 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 1994 in English and held by 16 WorldCat member libraries worldwide
The theory of algebraic number fields
by
David Hilbert(
Book
)
3 editions published in 1998 in English and held by 8 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
3 editions published in 1998 in English and held by 8 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
Séries de Kronecker et fonctions L des puissances symétriques de courbes elleptiques sur Q
by
JeanFrançois Mestre(
Book
)
2 editions published in 1989 in German and French and held by 2 WorldCat member libraries worldwide
2 editions published in 1989 in German and French and held by 2 WorldCat member libraries worldwide
Développement de la loi de groupe sur une cubique
by
Norbert Schappacher(
Book
)
2 editions published in 1990 in German and French and held by 2 WorldCat member libraries worldwide
2 editions published in 1990 in German and French and held by 2 WorldCat member libraries worldwide
Les conjectures de Beilinson pour les courbes elliptiques
by
Norbert Schappacher(
Book
)
2 editions published in 1989 in German and French and held by 2 WorldCat member libraries worldwide
2 editions published in 1989 in German and French and held by 2 WorldCat member libraries worldwide
Réduction de familles de points CM
by Christophe Cornut(
Book
)
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
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
Éléments explicites dans K2 d'une courbe elliptique
by
Klaus Rolshausen(
Book
)
2 editions published in 1996 in French and held by 2 WorldCat member libraries worldwide
SOIT E UNE COURBE ELLIPTIQUE DEFINIE SUR Q. LES CONJECTURES DE BLOCH ET BEILINSON PREDISENT LA VALEUR SPECIALE L(E, 2) ESSENTIELLEMENT EN TERME DE REGULATEURS D'ELEMENTS ENTIERS DU GROUPE K#2(E). LA METHODE LA PLUS RECENTE POUR CONSTRUIRE EXPLICITEMENT DE TELS ELEMENTS EST DUE A WILDESHAUS, DANS LE CADRE DE SON ANALOGUE ELLIPTIQUE DES CONJECTURES DE ZAGIER SUR LES POLYLOGARITHMES CLASSIQUES. NOUS SUIVONS LES PREMIERES ETAPES JUSQU'AU NIVEAU QUI CORRESPOND A LA VALEUR L(E,2) DU PROCEDE DE WILDESHAUS, TOUT EN FAISANT LA SYNTHESE AVEC UN TRAVAIL RECENT DE GONCHAROV ET LEVIN. IL S'AVERE QUE LA THEORIE CLASSIQUE DES COURBES ELLIPTIQUES SUFFIT POUR DEVELOPPER CE DEBUT DES CONJECTURES DE WILDESHAUS. NOUS VERIFIONS D'AILLEURS NUMERIQUEMENT CES CONJECTURES POUR QUELQUES COURBES QUI APPARAISSENT DANS LA FAMILLE A UN PARAMETRE DE COURBES ELLIPTIQUES SUR Q PROPOSEE PAR NEKOVAR DONT NOUS ETUDIONS L'ARITHMETIQUE. EN PARTICULIER NOUS MONTRONS QUE L'ELEMENT DISTINGUE DE K#2(E#A) QUI EXISTE PAR CONSTRUCTION DE LA FAMILLE, EST ENTIER SI ET SEULEMENT SI 12A APPARTIENT A Z
2 editions published in 1996 in French and held by 2 WorldCat member libraries worldwide
SOIT E UNE COURBE ELLIPTIQUE DEFINIE SUR Q. LES CONJECTURES DE BLOCH ET BEILINSON PREDISENT LA VALEUR SPECIALE L(E, 2) ESSENTIELLEMENT EN TERME DE REGULATEURS D'ELEMENTS ENTIERS DU GROUPE K#2(E). LA METHODE LA PLUS RECENTE POUR CONSTRUIRE EXPLICITEMENT DE TELS ELEMENTS EST DUE A WILDESHAUS, DANS LE CADRE DE SON ANALOGUE ELLIPTIQUE DES CONJECTURES DE ZAGIER SUR LES POLYLOGARITHMES CLASSIQUES. NOUS SUIVONS LES PREMIERES ETAPES JUSQU'AU NIVEAU QUI CORRESPOND A LA VALEUR L(E,2) DU PROCEDE DE WILDESHAUS, TOUT EN FAISANT LA SYNTHESE AVEC UN TRAVAIL RECENT DE GONCHAROV ET LEVIN. IL S'AVERE QUE LA THEORIE CLASSIQUE DES COURBES ELLIPTIQUES SUFFIT POUR DEVELOPPER CE DEBUT DES CONJECTURES DE WILDESHAUS. NOUS VERIFIONS D'AILLEURS NUMERIQUEMENT CES CONJECTURES POUR QUELQUES COURBES QUI APPARAISSENT DANS LA FAMILLE A UN PARAMETRE DE COURBES ELLIPTIQUES SUR Q PROPOSEE PAR NEKOVAR DONT NOUS ETUDIONS L'ARITHMETIQUE. EN PARTICULIER NOUS MONTRONS QUE L'ELEMENT DISTINGUE DE K#2(E#A) QUI EXISTE PAR CONSTRUCTION DE LA FAMILLE, EST ENTIER SI ET SEULEMENT SI 12A APPARTIENT A Z
Rational points : Seminar Bonn/Wuppertal 1983/84
by
Gerd Faltings(
Book
)
1 edition published in 1986 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1986 in English and held by 2 WorldCat member libraries worldwide
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(
Book
)
2 editions published in 2002 in German and held by 2 WorldCat member libraries worldwide
2 editions published in 2002 in German and held by 2 WorldCat member libraries worldwide
Der nahe und der ferne Euler
by
Norbert Schappacher(
)
1 edition published in 2007 in German and held by 1 WorldCat member library worldwide
1 edition published in 2007 in German and held by 1 WorldCat member library worldwide
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Audience Level
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Related Identities
 Schwermer, Joachim Editor
 Goldstein, Catherine (Mathematician) Author Editor
 Reznikov, Alexander 19602003 Author Editor
 Bernardi, Dominique Redactor Editor
 Tate, John Torrence 1925 Author
 Rapoport, M. 1948 Author Editor
 Schneider, P. (Peter) 1953 Editor
 Neukirch, Jürgen Author
 SpringerLink (Service en ligne)
 Koch, Helmut Editor
Associated Subjects
Algebra Algebra, Abstract Algebraic fields Algebraic number theory Arithmetic Beilinson's conjectures Congruences and residues Cyclotomy Differential equations, Partial Forms, Modular Geometry Geometry, Algebraic Germany GermanyBerlin Global differential geometry 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 Topology