1.

Record Nr.

UNINA9910452281303321

Autore

Eie Minking <1952->

Titolo

Theory of multiple Zeta values with applications in combinatorics [[electronic resource] /] / Minking Eie

Pubbl/distr/stampa

Hackensack, NJ, : World Scientific Pub., c2013

ISBN

981-4472-64-6

Descrizione fisica

1 online resource (313 p.)

Collana

Monographs in number theory ; ; v.7

Disciplina

510

512.73

515.56

Soggetti

Functions, Zeta

Algebraic functions

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Preface; Contents; I Basic Theory of Multiple Zeta Values; 0 The Time Before Multiple Zeta Values; 0.1 The Evaluation of Euler Double Sums; 0.2 Vandermonde Convolution; 0.3 Zeta Functions Associated with Multiple Zeta Values; 0.4 Messages from Modular Forms; 1 Introduction to the Theory of Multiple Zeta Values; 1.1 Introduction and Notations; 1.2 Drinfeld Integral Representations of Multiple Zeta Values; 1.3 Double Weighted Sum Formulas; 1.4 The Expectations of Binomial Distributions; 1.5 Exercises; 2 The Sum Formula; 2.1 Through the Integral Representations

2.2 Another Proof of the Sum Formula2.3 Evaluation of Multiple Zeta Values of Height One; 2.4 Exercises; II Shuffle Relations among Multiple Zeta Values; 3 Some Shuffle Relations; 3.1 Shuffle Relations of Multiple Zeta Values; 3.2 An Application of Double Weighted Sums; 3.3 Shuffle Relations of Two Sums of Multiple Zeta Values; 3.4 A Vector Version of the Restricted Sum Formula; 3.5 Exercises; 4 Euler Decomposition Theorem; 4.1 A Shuffle Relation with Two Parameters; 4.2 Integrals with Three Factors; 4.3 Generalizations of Euler Decomposition Theorem

4.4 Applications of the Decomposition Theorem4.5 Applications of



Another Decomposition Theorem; 4.6 Exercises; 5 Multiple Zeta Values of Height Two; 5.1 Sums of Multiple Zeta Values of Height Two; 5.2 Weighted Sums of Multiple Zeta Values of Height Two; 5.3 The Shuffle Product Formula of a Sum and Others; 5.4 Exercises; III Applications of Shuffle Relations in Combinatorics; 6 Generalizations of Pascal Identity; 6.1 Applications of Shuffle Products in Combinatorics; 6.2 Hypergeometric Distribution; 6.3 The Generating Function of Three Variables; 6.4 Exercises

7 Combinatorial Identities of Convolution Type7.1 Some Particular Combinatorial Identities; 7.2 A Generating Function for Products; 7.3 A Combinatorial Identity of Convolution Type; 7.4 Another Generating Function of Three Variables; 7.5 Exercises; 8 Vector Versions of Some Combinatorial Identities; 8.1 The Shuffle Product of Two Sums; 8.2 More Combinatorial Identities of Convolution Type; 8.3 Vector Versions of Pascal Identity; 8.4 Problems on Combinatorial Identity; Appendices; A Singular Modular Forms on the Exceptional Domain; A.1 Cayley Numbers and Integral Cayley Numbers

A.2 The Exceptional DomainA.3 The Theory of Jacobi Forms; A.4 A Final Application; Appendix (i): Jacobi Forms over Cayley Numbers; Appendix (ii): Basic Properties of a Set of Theta Series; B Shuffle Product Formulas of Multiple Zeta Values; B.1 Introduction; B.2 The Shuffle Product Formula of Two Multiple Zeta Values; B.3 Some Basic Shuffle Relations; B.4 Shuffle Relations of Two Sums of Multiple Zeta Values; B.5 The Generating Function of Height One; Appendix (i): Double Weighted Sum Formulas; Appendix (ii): Evaluations of Some Particular Integrals

C The Sum Formula and Their Generalizations

Sommario/riassunto

This is the first book on the theory of multiple zeta values since its birth around 1994. Readers will find that the shuffle products of multiple zeta values are applied to complicated counting problems in combinatorics, producing numerous interesting identities that are ready to be used. This will provide a powerful tool to deal with problems in multiple zeta values, both in evaluations and shuffle relations. The volume will benefit graduate students doing research in number theory.



2.

Record Nr.

UNISA996202532503316

Autore

Farley Daniel Scott

Titolo

Algebraic K-theory of Crystallographic Groups [[electronic resource] ] : The Three-Dimensional Splitting Case / / by Daniel Scott Farley, Ivonne Johanna Ortiz

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014

ISBN

3-319-08153-5

Edizione

[1st ed. 2014.]

Descrizione fisica

1 online resource (X, 148 p.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 2113

Disciplina

512.55

Soggetti

K-theory

Group theory

Manifolds (Mathematics)

Complex manifolds

K-Theory

Group Theory and Generalizations

Manifolds and Cell Complexes (incl. Diff.Topology)

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Sommario/riassunto

The Farrell-Jones isomorphism conjecture in algebraic K-theory offers a description of the algebraic K-theory of a group using a generalized homology theory. In cases where the conjecture is known to be a theorem, it gives a powerful method for computing the lower algebraic K-theory of a group. This book contains a computation of the lower algebraic K-theory of the split three-dimensional crystallographic groups, a geometrically important class of three-dimensional crystallographic group, representing a third of the total number. The book leads the reader through all aspects of the calculation. The first chapters describe the split crystallographic groups and their classifying spaces. Later chapters assemble the techniques that are needed to apply the isomorphism theorem. The result is a useful starting point for researchers who are interested in the computational side of the Farrell-Jones isomorphism conjecture, and a contribution to the growing



literature in the field.

3.

Record Nr.

UNINA9910791239303321

Autore

Jacoby Susan <1945->

Titolo

Alger Hiss and the battle for history [[electronic resource] /] / Susan Jacoby

Pubbl/distr/stampa

New Haven [Conn.], : Yale University Press, c2009

ISBN

1-282-50143-7

9786612501432

0-300-15584-0

1-4416-4560-8

Descrizione fisica

1 online resource (272 p.)

Collana

Icons of America

Disciplina

364.1/31

Soggetti

Communism - United States - History - 20th century

Espionage, Soviet - United States - History - 20th century

Cold War

Political culture - United States

Right and left (Political science)

United States Politics and government 1945-1989

United States Politics and government 1989-

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references (p. 231-242) and index.

Nota di contenuto

Frontmatter -- Contents -- Introduction -- One. Passions as Prologue -- Two. The Eye of the Hurricane, 1948-1950 -- Tree. Competing Narratives and Public Amnesia, 1950-1965 -- Four. The Best of Times, The Worst of Times, 1970-1980 -- Five. The Rise of the Right and the Cold War at Twilight, 1980-1992 -- Six. The Enemy Vanishes, 1992-2008 -- Conclusion. Passions as Epilogue -- Chronology -- Notes -- Selected Bibliography -- Acknowledgments -- Index

Sommario/riassunto

Books on Whittaker Chambers and Alger Hiss abound, as countless scholars have labored to uncover the facts behind Chambers's shocking accusation before the House Committee on Un-American Activities in



the summer of 1948-that Alger Hiss, a former rising star in the State Department, had been a Communist and engaged in espionage.In this highly original work, Susan Jacoby turns her attention to the Hiss case, including his trial and imprisonment for perjury, as a mirror of shifting American political views and passions. Unfettered by political ax-grinding, the author examines conflicting responses, from scholars and the media on both the left and the right, and the ways in which they have changed from 1948 to our present post-Cold War era. With a brisk, engaging style, Jacoby positions the case in the politics of the post-World War II era and then explores the ways in which generations of liberals and conservatives have put Chambers and Hiss to their own ideological uses. An iconic event of the McCarthy era, the case of Alger Hiss fascinates political intellectuals not only because of its historical significance but because of its timeless relevance to equally fierce debates today about the difficult balance between national security and respect for civil liberties.