Zagier, Don 1951
Overview
Works:  93 works in 262 publications in 5 languages and 2,791 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Interviewee, Other, Contributor, Creator 
Classifications:  QA3, 510.8 S 
Publication Timeline
.
Most widely held works by
Don Zagier
Equivariant Pontrjagin classes and applications to orbit spaces; applications of the Gsignature theorem to transformation
groups, symmetric products and number theory by
Don Zagier(
Book
)
24 editions published between 1942 and 2008 in 3 languages and held by 434 WorldCat member libraries worldwide
24 editions published between 1942 and 2008 in 3 languages and held by 434 WorldCat member libraries worldwide
Modular functions of one variable V : proceedings, international conference, University of Bonn, Sonderforschungsbereich
Theoretische Mathematik, July 214, 1976 by
JeanPierre Serre(
Book
)
51 editions published between 1976 and 2008 in 3 languages and held by 376 WorldCat member libraries worldwide
51 editions published between 1976 and 2008 in 3 languages and held by 376 WorldCat member libraries worldwide
The AtiyahSinger theorem and elementary number theory by
Friedrich Hirzebruch(
Book
)
15 editions published between 1974 and 1983 in English and held by 320 WorldCat member libraries worldwide
15 editions published between 1974 and 1983 in English and held by 320 WorldCat member libraries worldwide
The theory of Jacobi forms by
M Eichler(
Book
)
14 editions published in 1985 in English and held by 299 WorldCat member libraries worldwide
The functions studied in this monogra9h are a cross between elliptic functions and modular forms in one variable. Specifically, we define a Jacobi form on SL (~) to be a holomorphic function 2 (JC = upper halfplane) satisfying the t\10 transformation eouations 2Tiimcz k CT +d ar +b z ) (1) ( (cT+d) e cp(T,z) cp CT +d ' CT +d (2) rjl(T, z+h+]l) and having a Fourier expansion of the form 00 e2Tii(nT +rz) (3) cp(T,z) 2: c(n,r) 2:: rE~ n=O 2 r ~ 4nm Here k and m are natural numbers, called the weight and index of rp, respectively. Note that th e function cp (T, 0) is an ordinary modular formofweight k, whileforfixed T thefunction z+rjl(r,z) isa function of the type normally used to embed the elliptic curve ~/~T + ~ into a projective space. If m= 0, then cp is independent of z and the definition reduces to the usual notion of modular forms in one variable. We give three other examples of situations where functions satisfying (1)(3) arise classically: 1. Theta series. Let Q: ~+ ~ be a positive definite integer valued quadratic form and B the associated bilinear form
14 editions published in 1985 in English and held by 299 WorldCat member libraries worldwide
The functions studied in this monogra9h are a cross between elliptic functions and modular forms in one variable. Specifically, we define a Jacobi form on SL (~) to be a holomorphic function 2 (JC = upper halfplane) satisfying the t\10 transformation eouations 2Tiimcz k CT +d ar +b z ) (1) ( (cT+d) e cp(T,z) cp CT +d ' CT +d (2) rjl(T, z+h+]l) and having a Fourier expansion of the form 00 e2Tii(nT +rz) (3) cp(T,z) 2: c(n,r) 2:: rE~ n=O 2 r ~ 4nm Here k and m are natural numbers, called the weight and index of rp, respectively. Note that th e function cp (T, 0) is an ordinary modular formofweight k, whileforfixed T thefunction z+rjl(r,z) isa function of the type normally used to embed the elliptic curve ~/~T + ~ into a projective space. If m= 0, then cp is independent of z and the definition reduces to the usual notion of modular forms in one variable. We give three other examples of situations where functions satisfying (1)(3) arise classically: 1. Theta series. Let Q: ~+ ~ be a positive definite integer valued quadratic form and B the associated bilinear form
Die ersten 50 Millionen Primzahlen by
Don Zagier(
Book
)
12 editions published in 1977 in German and Undetermined and held by 149 WorldCat member libraries worldwide
12 editions published in 1977 in German and Undetermined and held by 149 WorldCat member libraries worldwide
Zetafunktionen und quadratische Körper : eine Eingührung in die höhere Zahlentheorie by
Don Zagier(
Book
)
15 editions published between 1981 and 2005 in 4 languages and held by 145 WorldCat member libraries worldwide
15 editions published between 1981 and 2005 in 4 languages and held by 145 WorldCat member libraries worldwide
Graphs on surfaces and their applications by
S. K Lando(
Book
)
6 editions published between 2003 and 2004 in English and held by 57 WorldCat member libraries worldwide
Graphs drawn on twodimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers
6 editions published between 2003 and 2004 in English and held by 57 WorldCat member libraries worldwide
Graphs drawn on twodimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers
Period functions for Maass wave forms and cohomology by
Roelof W Bruggeman(
Book
)
8 editions published in 2015 in English and held by 56 WorldCat member libraries worldwide
8 editions published in 2015 in English and held by 56 WorldCat member libraries worldwide
Lebendige Zahlen : fünf Exkursionen by
W Borho(
Book
)
3 editions published in 1981 in German and held by 47 WorldCat member libraries worldwide
Die Habilitation ist eine alte Einrichtung der deutschen Universi täten. Nachdem der junge Doktor nach der Promotion einige Jahre wissenschaftlich gearbeitet hat, legt er der Fakultät eine gröere Ver öffentlichung, die Habilitationsschrift, mit dem Ziel vor, die Venia Legendi zu erwerben, das Recht, in eigener Verantwortung zu lehren und Vorlesungen zu halten. Im Rahmen einer Fakultätssitzung fin den Habilitationsvortrag und wissenschaftliche Aussprache statt. Einige Wochen später wird das Verfahren durch die öffentliche An trittsvorlesung abgeschlossen, die zugleich den Höhepunkt darstellt. An manchen Universitäten scheint die Bedeutung der Antritts vorlesung zurückgegangen zu sein. In Bonn haben wir uns bemüht, diese Tradition fortzuftihren und die Antrittsvorlesungen zu einem wichtigen Teil des mathematischen Lebens zu machen. In den Vor trägen soll ein anspruchsvolles Thema so dargestellt werden, da Mathematiker und Naturwissenschaftler, die vielleicht in ganz ande ren Gebieten arbeiten, und auch Studenten, den Ausftihrungen fol gen können. Historische Entwicklungen und die Zusammenhänge der mathematischen Gebiete untereinander und mit Bereichen auer halb der Mathematik sollen erkennbar werden, den Zuhörern soll et was von der Faszination der Mathematik und ihrer Rolle im geisti gen Leben vermittelt werden
3 editions published in 1981 in German and held by 47 WorldCat member libraries worldwide
Die Habilitation ist eine alte Einrichtung der deutschen Universi täten. Nachdem der junge Doktor nach der Promotion einige Jahre wissenschaftlich gearbeitet hat, legt er der Fakultät eine gröere Ver öffentlichung, die Habilitationsschrift, mit dem Ziel vor, die Venia Legendi zu erwerben, das Recht, in eigener Verantwortung zu lehren und Vorlesungen zu halten. Im Rahmen einer Fakultätssitzung fin den Habilitationsvortrag und wissenschaftliche Aussprache statt. Einige Wochen später wird das Verfahren durch die öffentliche An trittsvorlesung abgeschlossen, die zugleich den Höhepunkt darstellt. An manchen Universitäten scheint die Bedeutung der Antritts vorlesung zurückgegangen zu sein. In Bonn haben wir uns bemüht, diese Tradition fortzuftihren und die Antrittsvorlesungen zu einem wichtigen Teil des mathematischen Lebens zu machen. In den Vor trägen soll ein anspruchsvolles Thema so dargestellt werden, da Mathematiker und Naturwissenschaftler, die vielleicht in ganz ande ren Gebieten arbeiten, und auch Studenten, den Ausftihrungen fol gen können. Historische Entwicklungen und die Zusammenhänge der mathematischen Gebiete untereinander und mit Bereichen auer halb der Mathematik sollen erkennbar werden, den Zuhörern soll et was von der Faszination der Mathematik und ihrer Rolle im geisti gen Leben vermittelt werden
Bernoulli numbers and Zeta functions by
Tsuneo Arakawa(
Book
)
7 editions published in 2014 in English and held by 43 WorldCat member libraries worldwide
Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausenvon Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of [rho]adic measures; the EulerMaclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of exponential sums expressed by generalized Bernoulli numbers; the relation between ideal classes of orders of quadratic fields and equivalence classes of binary quadratic forms; class number formula for positive definite binary quadratic forms; congruences between some class numbers and Bernoulli numbers; simple zeta functions of prehomogeneous vector spaces; Hurwitz numbers; Barnes multiple zeta functions and their special values; the functional equation of the double zeta functions; and polyBernoulli numbers. An appendix by Don Zagier on curious and exotic identities for Bernoulli numbers is also supplied. This book will be enjoyable both for amateurs and for professional researchers. Because the logical relations between the chapters are loosely connected, readers can start with any chapter depending on their interests. The expositions of the topics are not always typical, and some parts are completely new
7 editions published in 2014 in English and held by 43 WorldCat member libraries worldwide
Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausenvon Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of [rho]adic measures; the EulerMaclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of exponential sums expressed by generalized Bernoulli numbers; the relation between ideal classes of orders of quadratic fields and equivalence classes of binary quadratic forms; class number formula for positive definite binary quadratic forms; congruences between some class numbers and Bernoulli numbers; simple zeta functions of prehomogeneous vector spaces; Hurwitz numbers; Barnes multiple zeta functions and their special values; the functional equation of the double zeta functions; and polyBernoulli numbers. An appendix by Don Zagier on curious and exotic identities for Bernoulli numbers is also supplied. This book will be enjoyable both for amateurs and for professional researchers. Because the logical relations between the chapters are loosely connected, readers can start with any chapter depending on their interests. The expositions of the topics are not always typical, and some parts are completely new
Codierungstheorie und ihre Beziehung zu Geometrie und Zahlentheorie. : Primzahlen: Theorie und Anwendung / Don Zagier by
Friedrich Hirzebruch(
Book
)
4 editions published in 1989 in German and held by 40 WorldCat member libraries worldwide
4 editions published in 1989 in German and held by 40 WorldCat member libraries worldwide
Modular Functions of one Variable V : Proceedings International Conference, University of Bonn, Sonderforschungsbereich Theoretische
Mathematik July 214, 1976(
)
1 edition published in 1977 in English and held by 33 WorldCat member libraries worldwide
1 edition published in 1977 in English and held by 33 WorldCat member libraries worldwide
Modular Functions of One Variable VI : Proceedings International Conference, University of Bonn, Sonderforschungsbereich Theoretische
Mathematik July 214, 1976(
)
1 edition published in 1977 in English and held by 33 WorldCat member libraries worldwide
1 edition published in 1977 in English and held by 33 WorldCat member libraries worldwide
Leçon inaugurale : faite le jeudi 17 mai 2001, Collège de France, Chaire de théorie des nombres by
Don Zagier(
Book
)
1 edition published in 2001 in French and held by 28 WorldCat member libraries worldwide
1 edition published in 2001 in French and held by 28 WorldCat member libraries worldwide
Ground state of the quantum symmetric finite size XXZ spin chain with anisotropy parameter [delta] = 1/2 by
Vladislav Fridkin(
Book
)
2 editions published in 2000 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We find an analytic solution of the Bethe Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for U[subscript q](sl(2)) symmetry of the Hamiltonian. More precisely, we find one nontrivial solution, corresponding to the ground state of the system with anisotropy parameter [delta] = 1/2 corresponding to q = 1."
2 editions published in 2000 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We find an analytic solution of the Bethe Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for U[subscript q](sl(2)) symmetry of the Hamiltonian. More precisely, we find one nontrivial solution, corresponding to the ground state of the system with anisotropy parameter [delta] = 1/2 corresponding to q = 1."
Finite size XXZ spin chain with anisotropy parameter [delta] = 1/2 by
Vladislav Fridkin(
Book
)
2 editions published in 2000 in English and held by 3 WorldCat member libraries worldwide
Abstract: "We find an analytic solution of the Bethe Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for U[subscript q](sl(2)) symmetry of the Hamiltonian. More precisely, we find one nontrivial solution, corresponding to the ground state of the system with anisotropy parameter [delta] = 1/2 corresponding to q = 1. With a view to establishing an exact representation of the ground state of the finite size XXZ spin chain in terms of elementary functions, we concentrate on the crossingparameter [eta] dependence around [eta] = [pi]/3 for which there is a known solution. The approach taken involves the use of a physical solution Q of Baxter's tQ equation, corresponding to the ground state, as well as a nonphysical solution P of the same equation. The calculation of P and then of the ground state derivative is covered. Possible applications of this derivative to the theory of percolation have yet to be investigated. As far as the finite XXZ spin chain with periodic boundary conditions is concerned, we find a similar solution for an assymetric case which corresponds to the 6vertex model with a special magnetic field. For this case we find the analytic value of the 'magnetic moment' of the system in the corresponding state."
2 editions published in 2000 in English and held by 3 WorldCat member libraries worldwide
Abstract: "We find an analytic solution of the Bethe Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for U[subscript q](sl(2)) symmetry of the Hamiltonian. More precisely, we find one nontrivial solution, corresponding to the ground state of the system with anisotropy parameter [delta] = 1/2 corresponding to q = 1. With a view to establishing an exact representation of the ground state of the finite size XXZ spin chain in terms of elementary functions, we concentrate on the crossingparameter [eta] dependence around [eta] = [pi]/3 for which there is a known solution. The approach taken involves the use of a physical solution Q of Baxter's tQ equation, corresponding to the ground state, as well as a nonphysical solution P of the same equation. The calculation of P and then of the ground state derivative is covered. Possible applications of this derivative to the theory of percolation have yet to be investigated. As far as the finite XXZ spin chain with periodic boundary conditions is concerned, we find a similar solution for an assymetric case which corresponds to the 6vertex model with a special magnetic field. For this case we find the analytic value of the 'magnetic moment' of the system in the corresponding state."
Formes quasimodulaires sur des groupes modulaires cocompacts et restrictions des formes modulaires de Hilbert aux courbes
modulaires by
Najib Ouled Azaiez(
Book
)
1 edition published in 2005 in French and held by 3 WorldCat member libraries worldwide
1 edition published in 2005 in French and held by 3 WorldCat member libraries worldwide
Zhivye chisla : pi︠a︡tʹ ėkskursiĭ = Lebendige Zahlen(
Book
)
1 edition published in 1985 in Russian and held by 3 WorldCat member libraries worldwide
1 edition published in 1985 in Russian and held by 3 WorldCat member libraries worldwide
On the decomposability of the Gini coefficient and other indices of inequality by
Don Zagier(
Book
)
3 editions published in 1983 in German and English and held by 3 WorldCat member libraries worldwide
3 editions published in 1983 in German and English and held by 3 WorldCat member libraries worldwide
Miscellanea mathematica by
Michael Francis Atiyah(
)
1 edition published in 1991 in English and held by 0 WorldCat member libraries worldwide
Mathematics has a certain mystique, for it is pure and ex act, yet demands remarkable creativity. This reputation is reinforced by its characteristic abstraction and its own in dividual language, which often disguise its origins in and connections with the physical world. Publishing mathematics, therefore, requires special effort and talent. Heinz Gotze, who has dedicated his life to scientific pu blishing, took up this challenge with his typical enthusi asm. This Festschrift celebrates his invaluable contribu tions to the mathematical community, many of whose leading members he counts among his personal friends. The articles, written by mathematicians from around the world and coming from diverse fields, portray the important role of mathematics in our culture. Here, the reflections of important mathematicians, often focused on the history of mathematics, are collected, in recognition of Heinz Gotze's lifelong support of mathematics
1 edition published in 1991 in English and held by 0 WorldCat member libraries worldwide
Mathematics has a certain mystique, for it is pure and ex act, yet demands remarkable creativity. This reputation is reinforced by its characteristic abstraction and its own in dividual language, which often disguise its origins in and connections with the physical world. Publishing mathematics, therefore, requires special effort and talent. Heinz Gotze, who has dedicated his life to scientific pu blishing, took up this challenge with his typical enthusi asm. This Festschrift celebrates his invaluable contribu tions to the mathematical community, many of whose leading members he counts among his personal friends. The articles, written by mathematicians from around the world and coming from diverse fields, portray the important role of mathematics in our culture. Here, the reflections of important mathematicians, often focused on the history of mathematics, are collected, in recognition of Heinz Gotze's lifelong support of mathematics
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Related Identities
 Serre, JeanPierre 1926 Author Editor
 Hirzebruch, Friedrich Author
 Kaneko, Masanobu Contributor
 Arakawa, Tsuneo 19492003 Author
 Ibukiyama, Tomoyoshi Contributor
 Eichler, M. (Martin) Author
 Bruggeman, Roelof W. 1944 Author
 Lewis, J. (John B) 1944
 Lando, Sergei K. (1955....) Author
 Zvonkin, Alexander K.
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Associated Subjects
Algebra Algebraic number theory Algebraic topology Algorithms Bernoulli numbers Characteristic classes Coding theory Cohomology operations Combinatorial analysis Differential equations, Partial Embeddings (Mathematics) Errorcorrecting codes (Information theory) Fixed point theory Forms, Modular Forms, Quadratic Forms (Mathematics) Functional analysis Functions, Zeta Functions of complex variables Geometry Geometry, Algebraic Global analysis (Mathematics) Graph theory Group theory Hamiltonian systems Homology theory Jacobi forms Manifolds (Mathematics) Manybody problem Mappings (Mathematics) Mathematics Modular functions Numbers, Prime Number theory Pontryagin classes Quantum field theory Surfaces Symmetric functions Topology Transformation groups
Alternative Names
Don Zagier American mathematician
Don Zagier Amerikaans wiskundige
Don Zagier amerikansk matematikar
Don Zagier amerikansk matematiker
Don Zagier matematico statunitense
Don Zagier matematiker fra USA
Don Zagier mathmaticien amricain
Don Zagier USamerikanischer Mathematiker
Zagier, Bernard
Zagier Bernard 1951....
Zagier, D.
Zagier, D. 1951
Zagier, D. B.
Zagier, D. B. 1951
Zagier, D. B. (Don Bernard), 1951
Zagier, Don
Zagier, Don B.
Zagier, Don Bernard.
Zagier Don Bernard 1951....
Zagyā, D. B. 1951
Цагир, Дон
돈 재기어
ザギヤー, D. B
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