Sequences, Groups, and Number Theory

Sequences, Groups, and Number Theory
Author: Valérie Berthé
Publisher: Birkhäuser
Total Pages: 591
Release: 2018-04-09
Genre: Mathematics
ISBN: 331969152X

Download Sequences, Groups, and Number Theory Book in PDF, Epub and Kindle

This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.

Combinatorial Number Theory and Additive Group Theory

Combinatorial Number Theory and Additive Group Theory
Author: Alfred Geroldinger
Publisher: Springer Science & Business Media
Total Pages: 324
Release: 2009-04-15
Genre: Mathematics
ISBN: 3764389613

Download Combinatorial Number Theory and Additive Group Theory Book in PDF, Epub and Kindle

Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and which cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.

Numbers, Sequences and Series

Numbers, Sequences and Series
Author: Keith Hirst
Publisher: Elsevier
Total Pages: 213
Release: 1994-12-08
Genre: Mathematics
ISBN: 0080928587

Download Numbers, Sequences and Series Book in PDF, Epub and Kindle

Number and geometry are the foundations upon which mathematics has been built over some 3000 years. This book is concerned with the logical foundations of number systems from integers to complex numbers. The author has chosen to develop the ideas by illustrating the techniques used throughout mathematics rather than using a self-contained logical treatise. The idea of proof has been emphasised, as has the illustration of concepts from a graphical, numerical and algebraic point of view. Having laid the foundations of the number system, the author has then turned to the analysis of infinite processes involving sequences and series of numbers, including power series. The book also has worked examples throughout and includes some suggestions for self-study projects. In addition there are tutorial problems aimed at stimulating group work and discussion.

Uniform Distribution of Sequences

Uniform Distribution of Sequences
Author: L. Kuipers
Publisher: Courier Corporation
Total Pages: 416
Release: 2012-05-24
Genre: Mathematics
ISBN: 0486149994

Download Uniform Distribution of Sequences Book in PDF, Epub and Kindle

The theory of uniform distribution began with Hermann Weyl's celebrated paper of 1916. In later decades, the theory moved beyond its roots in diophantine approximations to provide common ground for topics as diverse as number theory, probability theory, functional analysis, and topological algebra. This book summarizes the theory's development from its beginnings to the mid-1970s, with comprehensive coverage of both methods and their underlying principles. A practical introduction for students of number theory and analysis as well as a reference for researchers in the field, this book covers uniform distribution in compact spaces and in topological groups, in addition to examinations of sequences of integers and polynomials. Notes at the end of each section contain pertinent bibliographical references and a brief survey of additional results. Exercises range from simple applications of theorems to proofs of propositions that expand upon results stated in the text.

Algebraic Groups and Number Theory

Algebraic Groups and Number Theory
Author: Vladimir Platonov
Publisher: Academic Press
Total Pages: 629
Release: 1993-12-07
Genre: Mathematics
ISBN: 0080874592

Download Algebraic Groups and Number Theory Book in PDF, Epub and Kindle

This milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number theory. The exposition of the topic is built on a synthesis of methods from algebraic geometry, number theory, analysis, and topology, and the result is a systematic overview ofalmost all of the major results of the arithmetic theory of algebraic groups obtained to date.

Automatic Sequences

Automatic Sequences
Author: Jean-Paul Allouche
Publisher: Cambridge University Press
Total Pages: 592
Release: 2003-07-21
Genre: Computers
ISBN: 9780521823326

Download Automatic Sequences Book in PDF, Epub and Kindle

Uniting dozens of seemingly disparate results from different fields, this book combines concepts from mathematics and computer science to present the first integrated treatment of sequences generated by 'finite automata'. The authors apply the theory to the study of automatic sequences and their generalizations, such as Sturmian words and k-regular sequences. And further, they provide applications to number theory (particularly to formal power series and transcendence in finite characteristic), physics, computer graphics, and music. Starting from first principles wherever feasible, basic results from combinatorics on words, numeration systems, and models of computation are discussed. Thus this book is suitable for graduate students or advanced undergraduates, as well as for mature researchers wishing to know more about this fascinating subject. Results are presented from first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and over 1600 citations to the literature.

Algebraic Groups and Number Theory: Volume 1

Algebraic Groups and Number Theory: Volume 1
Author: Vladimir Platonov
Publisher: Cambridge University Press
Total Pages: 380
Release: 2023-08-31
Genre: Mathematics
ISBN: 1009380656

Download Algebraic Groups and Number Theory: Volume 1 Book in PDF, Epub and Kindle

The first edition of this book provided the first systematic exposition of the arithmetic theory of algebraic groups. This revised second edition, now published in two volumes, retains the same goals, while incorporating corrections and improvements, as well as new material covering more recent developments. Volume I begins with chapters covering background material on number theory, algebraic groups, and cohomology (both abelian and non-abelian), and then turns to algebraic groups over locally compact fields. The remaining two chapters provide a detailed treatment of arithmetic subgroups and reduction theory in both the real and adelic settings. Volume I includes new material on groups with bounded generation and abstract arithmetic groups. With minimal prerequisites and complete proofs given whenever possible, this book is suitable for self-study for graduate students wishing to learn the subject as well as a reference for researchers in number theory, algebraic geometry, and related areas.

Combinatorial Group Theory, Discrete Groups, and Number Theory

Combinatorial Group Theory, Discrete Groups, and Number Theory
Author: Benjamin Fine
Publisher: American Mathematical Soc.
Total Pages: 282
Release: 2006
Genre: Mathematics
ISBN: 0821839853

Download Combinatorial Group Theory, Discrete Groups, and Number Theory Book in PDF, Epub and Kindle

This volume consists of contributions by participants and speakers at two conferences. The first was entitled Combinatorial Group Theory, Discrete Groups and Number Theory and was held at Fairfield University, December 8-9, 2004. It was in honor of Professor Gerhard Rosenberger's sixtieth birthday. The second was the AMS Special Session on Infinite Group Theory held at Bard College, October 8-9, 2005. The papers in this volume provide a very interesting mix of combinatorial group theory, discrete group theory and ring theory as well as contributions to noncommutative algebraic cryptography.

Recurrence Sequences

Recurrence Sequences
Author: Graham Everest
Publisher: American Mathematical Soc.
Total Pages: 338
Release: 2015-09-03
Genre: Mathematics
ISBN: 1470423154

Download Recurrence Sequences Book in PDF, Epub and Kindle

Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.

Modular Functions and Dirichlet Series in Number Theory

Modular Functions and Dirichlet Series in Number Theory
Author: Tom M. Apostol
Publisher: Springer Science & Business Media
Total Pages: 218
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461209994

Download Modular Functions and Dirichlet Series in Number Theory Book in PDF, Epub and Kindle

A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.