Surveys in Number Theory
Surveys in Number Theory

Author: Krishnaswami Alladi

Publisher: Springer Science & Business Media

Published: 2009-03-02

Total Pages: 193

ISBN-13: 0387785108

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Number theory has a wealth of long-standing problems, the study of which over the years has led to major developments in many areas of mathematics. This volume consists of seven significant chapters on number theory and related topics. Written by distinguished mathematicians, key topics focus on multipartitions, congruences and identities (G. Andrews), the formulas of Koshliakov and Guinand in Ramanujan's Lost Notebook (B. C. Berndt, Y. Lee, and J. Sohn), alternating sign matrices and the Weyl character formulas (D. M. Bressoud), theta functions in complex analysis (H. M. Farkas), representation functions in additive number theory (M. B. Nathanson), and mock theta functions, ranks, and Maass forms (K. Ono), and elliptic functions (M. Waldschmidt).

Surveys in Modern Mathematics
Surveys in Modern Mathematics

Author: Viktor Vasilʹevich Prasolov

Publisher: Cambridge University Press

Published: 2005-04-14

Total Pages: 360

ISBN-13: 0521547938

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Topics covered range from computational complexity, algebraic geometry, dynamics, through to number theory and quantum groups.

Surveys in Number Theory
Surveys in Number Theory

Author: Bruce Berndt

Publisher: CRC Press

Published: 2002-11-20

Total Pages: 368

ISBN-13: 1000065286

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This volume, based on fourteen papers from the Millennial Conference on Number Theory, represents surveys of topics in number theory and provides an outlook into the future of number theory research. It serves as an inspiration to graduate students and as a reference for research mathematicians.

Surveys in Set Theory
Surveys in Set Theory

Author: A. R. D. Mathias

Publisher: Cambridge University Press

Published: 1983-10-13

Total Pages: 257

ISBN-13: 0521277337

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This book comprises five expository articles and two research papers on topics of current interest in set theory and the foundations of mathematics. Articles by Baumgartner and Devlin introduce the reader to proper forcing. This is a development by Saharon Shelah of Cohen's method which has led to solutions of problems that resisted attack by forcing methods as originally developed in the 1960s. The article by Guaspari is an introduction to descriptive set theory, a subject that has developed dramatically in the last few years. Articles by Kanamori and Stanley discuss one of the most difficult concepts in contemporary set theory, that of the morass, first created by Ronald Jensen in 1971 to solve the gap-two conjecture in model theory, assuming Gödel's axiom of constructibility. The papers by Prikry and Shelah complete the volume by giving the reader the flavour of contemporary research in set theory. This book will be of interest to graduate students and research workers in set theory and mathematical logic.

Numerical Algorithms for Number Theory: Using Pari/GP
Numerical Algorithms for Number Theory: Using Pari/GP

Author: Karim Belabas

Publisher: American Mathematical Soc.

Published: 2021-06-23

Total Pages: 429

ISBN-13: 1470463512

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This book presents multiprecision algorithms used in number theory and elsewhere, such as extrapolation, numerical integration, numerical summation (including multiple zeta values and the Riemann-Siegel formula), evaluation and speed of convergence of continued fractions, Euler products and Euler sums, inverse Mellin transforms, and complex L L-functions. For each task, many algorithms are presented, such as Gaussian and doubly-exponential integration, Euler-MacLaurin, Abel-Plana, Lagrange, and Monien summation. Each algorithm is given in detail, together with a complete implementation in the free Pari/GP system. These implementations serve both to make even more precise the inner workings of the algorithms, and to gently introduce advanced features of the Pari/GP language. This book will be appreciated by anyone interested in number theory, specifically in practical implementations, computer experiments and numerical algorithms that can be scaled to produce thousands of digits of accuracy.

Introduction to Modern Number Theory
Introduction to Modern Number Theory

Author: Yu. I. Manin

Publisher: Springer Science & Business Media

Published: 2006-03-30

Total Pages: 519

ISBN-13: 3540276920

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This edition has been called ‘startlingly up-to-date’, and in this corrected second printing you can be sure that it’s even more contemporaneous. It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory. Illuminated by elementary problems, the central ideas of modern theories are laid bare. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories.

Surveys in Geometry and Number Theory
Surveys in Geometry and Number Theory

Author: Nicholas Young

Publisher: Cambridge University Press

Published: 2007-01-18

Total Pages: 327

ISBN-13: 0521691826

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A collection of survey articles by leading young researchers, showcasing the vitality of Russian mathematics.

Surveys in Contemporary Mathematics
Surveys in Contemporary Mathematics

Author: Nicholas Young

Publisher: Cambridge University Press

Published: 2008

Total Pages: 370

ISBN-13: 0521705649

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A collection of articles showcasing the achievements of young Russian researchers in combinatorial and algebraic geometry and topology.

Number Theory and Related Fields
Number Theory and Related Fields

Author: Jonathan M. Borwein

Publisher: Springer Science & Business Media

Published: 2013-05-16

Total Pages: 395

ISBN-13: 1461466423

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“Number Theory and Related Fields” collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van der Poorten," hosted by CARMA and held March 12-16th 2012 at the University of Newcastle, Australia. The purpose of the conference was to promote number theory research in Australia while commemorating the legacy of Alf van der Poorten, who had written over 170 papers on the topic of number theory and collaborated with dozens of researchers. The research articles and surveys presented in this book were written by some of the most distinguished mathematicians in the field of number theory, and articles will include related topics that focus on the various research interests of Dr. van der Poorten.​