Pisot And Salem Numbers

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Pisot and Salem Numbers

Author : Marie J. Bertin
Publisher : Birkhäuser
ISBN 13 : 3034886322
Total Pages : 297 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Pisot and Salem Numbers by : Marie J. Bertin

Download or read book Pisot and Salem Numbers written by Marie J. Bertin and published by Birkhäuser. This book was released on 2012-12-06 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: the attention of The publication of Charles Pisot's thesis in 1938 brought to the mathematical community those marvelous numbers now known as the Pisot numbers (or the Pisot-Vijayaraghavan numbers). Although these numbers had been discovered earlier by A. Thue and then by G. H. Hardy, it was Pisot's result in that paper of 1938 that provided the link to harmonic analysis, as discovered by Raphael Salem and described in a series of papers in the 1940s. In one of these papers, Salem introduced the related class of numbers, now universally known as the Salem numbers. These two sets of algebraic numbers are distinguished by some striking arith metic properties that account for their appearance in many diverse areas of mathematics: harmonic analysis, ergodic theory, dynamical systems and alge braic groups. Until now, the best known and most accessible introduction to these num bers has been the beautiful little monograph of Salem, Algebraic Numbers and Fourier Analysis, first published in 1963. Since the publication of Salem's book, however, there has been much progress in the study of these numbers. Pisot had long expressed the desire to publish an up-to-date account of this work, but his death in 1984 left this task unfulfilled.

Pisot and Salem Numbers

Author : Marie José Bertin
Publisher : Birkhauser
ISBN 13 : 9780817626488
Total Pages : 291 pages
Book Rating : 4.6/5 (264 download)

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Book Synopsis Pisot and Salem Numbers by : Marie José Bertin

Download or read book Pisot and Salem Numbers written by Marie José Bertin and published by Birkhauser. This book was released on 1992 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computational Excursions in Analysis and Number Theory

Author : Peter Borwein
Publisher : Springer Science & Business Media
ISBN 13 : 0387216529
Total Pages : 220 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Computational Excursions in Analysis and Number Theory by : Peter Borwein

Download or read book Computational Excursions in Analysis and Number Theory written by Peter Borwein and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included.

Around the Unit Circle

Author : James McKee
Publisher : Springer Nature
ISBN 13 : 3030800318
Total Pages : 444 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Around the Unit Circle by : James McKee

Download or read book Around the Unit Circle written by James McKee and published by Springer Nature. This book was released on 2021-12-08 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject of several longstanding unsolved questions, such as Lehmer’s Problem (1933) and Boyd’s Conjecture (1981). This book contains a wide range of results on Mahler measure. Some of the results are very recent, such as Dimitrov’s proof of the Schinzel–Zassenhaus Conjecture. Other known results are included with new, streamlined proofs. Robinson’s Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are also discussed, for the first time in a book. One way to study algebraic integers is to associate them with combinatorial objects, such as integer matrices. In some of these combinatorial settings the analogues of several notorious open problems have been solved, and the book sets out this recent work. Many Mahler measure results are proved for restricted sets of polynomials, such as for totally real polynomials, and reciprocal polynomials of integer symmetric as well as symmetrizable matrices. For reference, the book includes appendices providing necessary background from algebraic number theory, graph theory, and other prerequisites, along with tables of one- and two-variable integer polynomials with small Mahler measure. All theorems are well motivated and presented in an accessible way. Numerous exercises at various levels are given, including some for computer programming. A wide range of stimulating open problems is also included. At the end of each chapter there is a glossary of newly introduced concepts and definitions. Around the Unit Circle is written in a friendly, lucid, enjoyable style, without sacrificing mathematical rigour. It is intended for lecture courses at the graduate level, and will also be a valuable reference for researchers interested in Mahler measure. Essentially self-contained, this textbook should also be accessible to well-prepared upper-level undergraduates.

Number Theory

Author : Canadian Number Theory Association. Conference
Publisher : American Mathematical Soc.
ISBN 13 : 9780821873274
Total Pages : 430 pages
Book Rating : 4.8/5 (732 download)

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Book Synopsis Number Theory by : Canadian Number Theory Association. Conference

Download or read book Number Theory written by Canadian Number Theory Association. Conference and published by American Mathematical Soc.. This book was released on 1999-01-01 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers presented at the fifth Canadian Number Theory Association (CNTA) conference held at Carleton University (Ottawa, ON). The invited speakers focused on arithmetic algebraic geometry and elliptic curves, diophantine problems, analytic number theory, and algebraic and computational number theory. The contributed talks represented a wide variety of areas in number theory. David Boyd gave an hour-long talk on "Mahler's Measure and Elliptic Curves". This lecture was open to the public and attracted a large audience from outside the conference.

Distribution Modulo One and Diophantine Approximation

Author : Yann Bugeaud
Publisher : Cambridge University Press
ISBN 13 : 0521111692
Total Pages : 317 pages
Book Rating : 4.5/5 (211 download)

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Book Synopsis Distribution Modulo One and Diophantine Approximation by : Yann Bugeaud

Download or read book Distribution Modulo One and Diophantine Approximation written by Yann Bugeaud and published by Cambridge University Press. This book was released on 2012-07-05 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: A treatment of cutting-edge research on the distribution modulo one of sequences and related topics, much of it from the last decade. There are numerous exercises to aid student understanding of the topic, and researchers will appreciate the notes at the end of each chapter, extensive references and open problems.

Birds and Frogs

Author : Freeman J Dyson
Publisher : World Scientific Publishing Company
ISBN 13 : 9814602876
Total Pages : 375 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Birds and Frogs by : Freeman J Dyson

Download or read book Birds and Frogs written by Freeman J Dyson and published by World Scientific Publishing Company. This book was released on 2015-03-25 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a sequel to the volume of selected papers of Dyson up to 1990 that was published by the American Mathematical Society in 1996. The present edition comprises a collection of the most interesting writings of Freeman Dyson, all personally selected by the author, from the period 1990–2014. The five sections start off with an Introduction, followed by Talks about Science, Memoirs, Politics and History, and some Technical Papers. The most noteworthy is a lecture entitled Birds and Frogs to the American Mathematical Society that describes two kinds of mathematicians with examples from real life. Other invaluable contributions include an important tribute to C. N. Yang written for his retirement banquet at Stony Brook University, as well as a historical account of the Operational Research at RAF Bomber Command in World War II provocatively titled A Failure of Intelligence. The final section carries the open-ended question of whether any conceivable experiment could detect single gravitons to provide direct evidence of the quantization of gravity — Is a Graviton Detectable? Various possible graviton-detectors are examined. This invaluable compilation contains unpublished lectures, and surveys many topics in science, mathematics, history and politics, in which Freeman Dyson has been so active and well respected around the world.

Fractal Geometry and Stochastics II

Author : Christoph Bandt
Publisher : Springer Science & Business Media
ISBN 13 : 9783764362157
Total Pages : 308 pages
Book Rating : 4.3/5 (621 download)

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Book Synopsis Fractal Geometry and Stochastics II by : Christoph Bandt

Download or read book Fractal Geometry and Stochastics II written by Christoph Bandt and published by Springer Science & Business Media. This book was released on 2000-02-14 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of contributions by outstanding mathematicians, highlighting the principal directions of research on the combination of fractal geometry and stochastic methods. Clear expositions introduce the most recent results and problems on these subjects and give an overview of their historical development.

Encyclopaedia of Mathematics

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 9401512795
Total Pages : 639 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Fractals in Probability and Analysis

Author : Christopher J. Bishop
Publisher : Cambridge University Press
ISBN 13 : 1107134110
Total Pages : 415 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Fractals in Probability and Analysis by : Christopher J. Bishop

Download or read book Fractals in Probability and Analysis written by Christopher J. Bishop and published by Cambridge University Press. This book was released on 2017 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.

Algebraic Numbers and Harmonic Analysis

Author :
Publisher : Elsevier
ISBN 13 : 008095412X
Total Pages : 285 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Algebraic Numbers and Harmonic Analysis by :

Download or read book Algebraic Numbers and Harmonic Analysis written by and published by Elsevier. This book was released on 2000-04-01 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Numbers and Harmonic Analysis

The Cremona Group and Its Subgroups

Author : Julie Déserti
Publisher : American Mathematical Soc.
ISBN 13 : 1470460122
Total Pages : 187 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Cremona Group and Its Subgroups by : Julie Déserti

Download or read book The Cremona Group and Its Subgroups written by Julie Déserti and published by American Mathematical Soc.. This book was released on 2021-04-13 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to present a portrait of the n n-dimensional Cremona group with an emphasis on the 2-dimensional case. After recalling some crucial tools, the book describes a naturally defined infinite dimensional hyperbolic space on which the Cremona group acts. This space plays a fundamental role in the study of Cremona groups, as it allows one to apply tools from geometric group theory to explore properties of the subgroups of the Cremona group as well as the degree growth and dynamical behavior of birational transformations. The book describes natural topologies on the Cremona group, codifies the notion of algebraic subgroups of the Cremona groups and finishes with a chapter on the dynamics of their actions. This book is aimed at graduate students and researchers in algebraic geometry who are interested in birational geometry and its interactions with geometric group theory and dynamical systems.

Number Theory in Progress

Author : Kálmán Györy
Publisher : Walter de Gruyter
ISBN 13 : 3110285584
Total Pages : 1212 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Number Theory in Progress by : Kálmán Györy

Download or read book Number Theory in Progress written by Kálmán Györy and published by Walter de Gruyter. This book was released on 2012-02-13 with total page 1212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the International Conference on Number Theory organized by the Stefan Banach International Mathematical Center in Honor of the 60th Birthday of Andrzej Schinzel, Zakopane, Poland, June 30-July 9, 1997.

Computer Algebra 2006

Author : Ilias Kotsireas
Publisher : World Scientific
ISBN 13 : 9812702008
Total Pages : 220 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Computer Algebra 2006 by : Ilias Kotsireas

Download or read book Computer Algebra 2006 written by Ilias Kotsireas and published by World Scientific. This book was released on 2007 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by world-renowned experts, the book is a collection of tutorial presentations and research papers catering to the latest advances in symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. The papers were presented at a workshop celebrating the 60th birthday of Sergei Abramov (Russia), whose highly influential contributions to symbolic methods are adopted in many leading computer algebra systems.

Latest Advances in Symbolic Algorithms

Author : Ilias Kotsireas
Publisher : World Scientific
ISBN 13 : 9812778853
Total Pages : 220 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Latest Advances in Symbolic Algorithms by : Ilias Kotsireas

Download or read book Latest Advances in Symbolic Algorithms written by Ilias Kotsireas and published by World Scientific. This book was released on 2007 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by world-renowned experts, the book is a collection of tutorial presentations and research papers catering to the latest advances in symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. The papers were presented at a workshop celebrating the 60th birthday of Sergei Abramov (Russia), whose highly influential contributions to symbolic methods are adopted in many leading computer algebra systems.

Geometry of Polynomials

Author : Morris Marden
Publisher : American Mathematical Soc.
ISBN 13 : 0821815032
Total Pages : 260 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometry of Polynomials by : Morris Marden

Download or read book Geometry of Polynomials written by Morris Marden and published by American Mathematical Soc.. This book was released on 1949-12-31 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the years since the first edition of this well-known monograph appeared, the subject (the geometry of the zeros of a complex polynomial) has continued to display the same outstanding vitality as it did in the first 150 years of its history, beginning with the contributions of Cauchy and Gauss. Thus, the number of entries in the bibliography of this edition had to be increased from about 300 to about 600 and the book enlarged by one third. It now includes a more extensive treatment of Hurwitz polynomials and other topics. The new material on infrapolynomials, abstract polynomials, and matrix methods is of particular interest.

Number Theory

Author : Richard Mollin
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110848635
Total Pages : 676 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Number Theory by : Richard Mollin

Download or read book Number Theory written by Richard Mollin and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-12-19 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.