Author: Leonard Lewin

Publisher: American Mathematical Soc.

ISBN: 0821816349

Category: Mathematics

Page: 412

View: 1815

Skip to content
#
Search Results for: structural-properties-of-polylogarithms-mathematical-surveys-and-monographs

## Structural Properties of Polylogarithms

Years ago, the handful of peculiar numerical dilogarithmic identities, known since the time of Euler and Landen, gave rise to new discoveries concerning cyclotomic equations and related polylogarithmic ladders. These discoveries were made mostly by the methods of classical analysis, with help from machine computation. About the same time, starting with Bloch's studies on the application of the dilogarithm in algebraic $K$-theory and algebraic geometry, many important discoveries were made in diverse areas.This book seeks to provide a synthesis of these two streams of thought. In addition to an account of ladders and their association with functional equations, the chapters include applications to volume calculations in Lobatchevsky geometry, relations to partition theory, connections with Clausen's function, new functional equations, and applications to $K$-theory and other branches of abstract algebra. This rapidly-expanding field is brought up to date with two appendices, and the book concludes with an extensive bibliography of recent publications. About two-thirds of the material is accessible to mathematicians and scientists in many areas, while the remainder requires more specialized background in abstract algebra.
## Structural Properties of Polylogarithms

Years ago, the handful of peculiar numerical dilogarithmic identities, known since the time of Euler and Landen, gave rise to new discoveries concerning cyclotomic equations and related polylogarithmic ladders. These discoveries were made mostly by the methods of classical analysis, with help from machine computation. About the same time, starting with Bloch's studies on the application of the dilogarithm in algebraic $K$-theory and algebraic geometry, many important discoveries were made in diverse areas.This book seeks to provide a synthesis of these two streams of thought. In addition to an account of ladders and their association with functional equations, the chapters include applications to volume calculations in Lobatchevsky geometry, relations to partition theory, connections with Clausen's function, new functional equations, and applications to $K$-theory and other branches of abstract algebra. This rapidly-expanding field is brought up to date with two appendices, and the book concludes with an extensive bibliography of recent publications. About two-thirds of the material is accessible to mathematicians and scientists in many areas, while the remainder requires more specialized background in abstract algebra.
## The Arithmetic of Fundamental Groups

In the more than 100 years since the fundamental group was first introduced by Henri Poincaré it has evolved to play an important role in different areas of mathematics. Originally conceived as part of algebraic topology, this essential concept and its analogies have found numerous applications in mathematics that are still being investigated today, and which are explored in this volume, the result of a meeting at Heidelberg University that brought together mathematicians who use or study fundamental groups in their work with an eye towards applications in arithmetic. The book acknowledges the varied incarnations of the fundamental group: pro-finite, l-adic, p-adic, pro-algebraic and motivic. It explores a wealth of topics that range from anabelian geometry (in particular the section conjecture), the l-adic polylogarithm, gonality questions of modular curves, vector bundles in connection with monodromy, and relative pro-algebraic completions, to a motivic version of Minhyong Kim's non-abelian Chabauty method and p-adic integration after Coleman. The editor has also included the abstracts of all the talks given at the Heidelberg meeting, as well as the notes on Coleman integration and on Grothendieck's fundamental group with a view towards anabelian geometry taken from a series of introductory lectures given by Amnon Besser and Tamás Szamuely, respectively.
## Zeta and q-Zeta Functions and Associated Series and Integrals

Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals. Detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions
## Series Associated With the Zeta and Related Functions

Designed as a reference work and also as a graduate-level textbook, this volume presents an up-to-date and comprehensive account of the theories and applications of the various methods and techniques used in dealing with problems involving closed-form evaluations of (and representations of the Riemann Zeta function at positive integer arguments as) numerous families of series associated with the Riemann Zeta function, the Hurwitz Zeta function, and their extensions and generalizations such as Lerch's transcendent (or the Hurwitz-Lerch Zeta function). Audience: This book is intended for professional mathematicians and graduate students in mathematical sciences (both pure and applied).
## Congruences for L-Functions

This book provides a comprehensive and up-to-date treatment of research carried out in the last twenty years on congruences involving the values of L-functions (attached to quadratic characters) at certain special values. There is no other book on the market which deals with this subject. The book presents in a unified way congruences found by many authors over the years, from the classical ones of Gauss and Dirichlet to the recent ones of Gras, Vehara, and others. Audience: This book is aimed at graduate students and researchers interested in (analytic) number theory, functions of a complex variable and special functions.
## Notices of the American Mathematical Society

## Nagoya Mathematical Journal

## The arithmetic and geometry of algebraic cycles

The subject of algebraic cycles has thrived through its interaction with algebraic K-theory, Hodge theory, arithmetic algebraic geometry, number theory, and topology. These interactions have led to such developments as a description of Chow groups in terms of algebraic K-theory, the arithmetic Abel-Jacobi mapping, progress on the celebrated conjectures of Hodge and Tate, and the conjectures of Bloch and Beilinson. The immense recent progress in algebraic cycles, based on so many interactions with so many other areas of mathematics, has contributed to a considerable degree of inaccessibility, especially for graduate students. Even specialists in one approach to algebraic cycles may not understand other approaches well. This book offers students and specialists alike a broad perspective of algebraic cycles, presented from several viewpoints, including arithmetic, transcendental, topological, motives and K-theory methods. Topics include a discussion of the arithmetic Abel-Jacobi mapping, higher Abel-Jacobi regulator maps, polylogarithms and L-series, candidate Bloch-Beilinson filtrations, applications of Chern-Simons invariants to algebraic cycles via the study of algebraic vector bundles with algebraic connection, motivic cohomology, Chow groups of singular varieties, and recent progress on the Hodge and Tate conjectures for Abelian varieties.
## Beiträge Zur Algebra und Geometrie

## Conformal invariants, inequalities, and quasiconformal maps

A unified view of conformal invariants from the point of view of applications in geometric function theory and applications and quasiconformal mappings in the plane and in space.
## Reviews in Number Theory, 1984-96

These six volumes include approximately 20,000 reviews of items in number theory that appeared in Mathematical Reviews between 1984 and 1996. This is the third such set of volumes in number theory. The first was edited by W.J. LeVeque and included reviews from 1940-1972; the second was edited by R.K. Guy and appeared in 1984.
## Annales Polonici mathematici

## Combined Membership List of the American Mathematical Society and the Mathematical Association of America

Lists for 19 include the Mathematical Association of America, and 1955- also the Society for Industrial and Applied Mathematics.
## Abstracts of Papers Presented to the American Mathematical Society

## New Technical Books

## Who's who in European Research and Development

## Introduction to the Theory of Algebraic Functions of One Variable

Presents an approach to algebraic geometry of curves that is treated as the theory of algebraic functions on the curve. This book discusses such topics as the theory of divisors on a curve, the Riemann-Roch theorem, $p$-adic completion, and extensions of the fields of functions (covering theory) and of the fields of constants.
## The Markoff and Lagrange Spectra

This book is directed at mathematicians interested in Diophantine approximation and the theory of quadratic forms and the relationship of these subjects to Markoff and Lagrange spectra. The authors have gathered and systemized numerous results from the diverse and scattered literature, much of which has appeared in rather inaccessible Russian publications. Readers will find a comprehensive overview of the theory of the Markoff and Lagrange spectra, starting with the origins of the subject in two papers of A. Markoff from 1879-80. Most of the progress since that time has occurred in the last 20 years or so, when there has been a resurgence of interest in these spectra. The authors provide an excellent exposition of these developments, in addition to presenting many proofs and correcting various errors in the literature.
## Geometric Approximation Algorithms

Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.

Full PDF eBook Download Free

Author: Leonard Lewin

Publisher: American Mathematical Soc.

ISBN: 0821816349

Category: Mathematics

Page: 412

View: 1815

Author: Leonard Lewin

Publisher: American Mathematical Soc.

ISBN: 9780821816349

Category: Mathematics

Page: 412

View: 3978

*PIA 2010*

Author: Jakob Stix

Publisher: Springer Science & Business Media

ISBN: 3642239056

Category: Mathematics

Page: 380

View: 2607

Author: H. M. Srivastava,Junesang Choi

Publisher: Elsevier

ISBN: 0123852196

Category: Mathematics

Page: 674

View: 9838

Author: H. M. Srivastava,Choi Junesang

Publisher: Springer Science & Business Media

ISBN: 9780792370543

Category: Mathematics

Page: 388

View: 700

Author: J. Urbanowicz,Kenneth S. Williams

Publisher: Springer Science & Business Media

ISBN: 9780792363798

Category: Mathematics

Page: 256

View: 6912

Author: American Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 2551

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 7623

Author: B. Brent Gordon

Publisher: Kluwer Academic Pub

ISBN: N.A

Category: Mathematics

Page: 615

View: 8281

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Algebra

Page: N.A

View: 2375

Author: Glen Douglas Anderson,Mavina Krishna Vamanamurthy,Matti Vuorinen

Publisher: Wiley-Interscience

ISBN: N.A

Category: Mathematics

Page: 505

View: 2826

*As Printed in Mathematical Reviews*

Author: N.A

Publisher: Amer Mathematical Society

ISBN: 9780821809365

Category: Mathematics

Page: 764

View: 4723

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 2656

Author: American Mathematical Society

Publisher: N.A

ISBN: 9780821801703

Category: Mathematics

Page: 587

View: 7328

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 4375

Author: New York Public Library

Publisher: N.A

ISBN: N.A

Category: Engineering

Page: N.A

View: 9891

Author: European research and development database

Publisher: N.A

ISBN: 9783598115769

Category: Science

Page: 1097

View: 9699

Author: Claude Chevalley

Publisher: American Mathematical Soc.

ISBN: 0821815067

Category: Mathematics

Page: 188

View: 8557

Author: Thomas W. Cusick,Mary E. Flahive

Publisher: American Mathematical Soc.

ISBN: 0821815318

Category: Mathematics

Page: 97

View: 6671

Author: Sariel Har-Peled

Publisher: American Mathematical Soc.

ISBN: 0821849115

Category: Mathematics

Page: 362

View: 7979