WorldCat Identities

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
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Most widely held works by Don Zagier
Equivariant Pontrjagin classes and applications to orbit spaces; applications of the G-signature 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

Modular functions of one variable V- : proceedings, international conference, University of Bonn, Sonderforschungsbereich Theoretische Mathematik, July 2-14, 1976 by Jean-Pierre Serre( Book )

51 editions published between 1976 and 2008 in 3 languages and held by 376 WorldCat member libraries worldwide

The Atiyah-Singer 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

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 half-plane) satisfying the t\-10 transformation eouations 2Tiimcz k CT +d a-r +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

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

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 two-dimensional 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

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
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 Clausen-von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of [rho]-adic measures; the Euler-Maclaurin 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 poly-Bernoulli 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

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

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."
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 crossing-parameter [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 t-Q equation, corresponding to the ground state, as well as a non-physical 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 6-vertex 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 quasi-modulaires sur des groupes modulaires co-compacts 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

Zhivye chisla : pi︠a︡tʹ ėkskursiĭ = Lebendige Zahlen( Book )

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

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 life-long support of mathematics
 
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Audience level: 0.72 (from 0.52 for Bernoulli ... to 0.96 for On the dec ...)

Equivariant Pontrjagin classes and applications to orbit spaces; applications of the G-signature theorem to transformation groups, symmetric products and number theory
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 US-amerikanischer 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

Languages
English (128)

German (31)

Japanese (3)

French (2)

Russian (1)

Covers
Modular functions of one variable V- : proceedings, international conference, University of Bonn, Sonderforschungsbereich Theoretische Mathematik, July 2-14, 1976The Atiyah-Singer theorem and elementary number theoryZetafunktionen und quadratische Körper : eine Eingührung in die höhere ZahlentheorieGraphs on surfaces and their applicationsModular Functions of one Variable V : Proceedings International Conference, University of Bonn, Sonderforschungsbereich Theoretische Mathematik July 2-14, 1976Modular Functions of One Variable VI : Proceedings International Conference, University of Bonn, Sonderforschungsbereich Theoretische Mathematik July 2-14, 1976