Number Theory

Number theory, the branch of mathematics which studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. The authors have gathered together a collection of problems from various...

This book is an introduction to algebraic number theory via the famous problem of "Fermat's Last Theorem." The exposition follows the historical development of the problem, beginning with the work of Fermat and ending with Kummer's theory of "ideal"...

Number Theory or arithmetic, as some prefer to call it, is the oldest, purest, liveliest, most elementary yet sophisticated field of mathematics. It is no coincidence that the fundamental science of numbers has come to be known as the "Queen of...

Elementary Number Theory, Gove Effinger, Gary L. MullenThis text is intended to be used as an undergraduate introduction to the theory of numbers. The authors have been immersed in this area of mathematics for many years and hope that this text will...

From Polynomials to Sums of Squares describes a journey through the foothills of algebra and number theory based around the central theme of factorization. The book begins by providing basic knowledge of rational polynomials, then gradually introduces...

This graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. Definitions are kept to a minimum and repeated when reintroduced so that the...

The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete...

This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite...

The computation of invariants of algebraic number fields such as integral bases, discriminants, prime decompositions, ideal class groups, and unit groups is important both for its own sake and for its numerous applications, for example, to the solution...

This textbook offers an introduction to abelian varieties, a rich topic of central importance to algebraic geometry. The emphasis is on geometric constructions over the complex numbers, notably the construction of important classes of abelian varieties...

Elementary number theory is concerned with the arithmetic properties of the ring of integers, Z, and its field of fractions, the rational numbers, Q. Early on in the development of the subject it was noticed that Z has many properties in common with A =...

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the...

Atle Selberg's early work, which lies in the fields of analysis and number theory, concerns the Riemann zeta-function, Dirichlet's L-functions, the Fourier coefficients of modular forms, the distribution of prime numbers and the general sieve method. It...

In its first six chapters this 2006 text seeks to present the basic ideas and properties of the Jacobi elliptic functions as an historical essay, an attempt to answer the fascinating question: 'what would the treatment of elliptic functions have been...

This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory. The ancient "congruent number problem" is the central motivating example for most of the book. My purpose is to make...

This introduction to automorphic forms on adelic groups G(A) emphasises the role of representation theory. The exposition is driven by examples, and collects and extends many results scattered throughout the literature, in particular the Langlands...

This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some...

Diophantine geometry has been studied by number theorists for thousands of years, since the time of Pythagoras, and has continued to be a rich area of ideas such as Fermat's Last Theorem, and most recently the ABC conjecture. This monograph is a bridge...

The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the...

Volume II provides an advanced approach to the extended gibonacci family, which includes Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas, Vieta, Vieta-Lucas, and Chebyshev polynomials of both kinds. This volume offers a uniquely unified,...

This introduction to algebraic number theory via the famous problem of "Fermats Last Theorem" follows its historical development, beginning with the work of Fermat and ending with Kummers theory of "ideal" factorization. The more...

A study of how complexity questions in computing interact with classical mathematics in the numerical analysis of issues in algorithm design. Algorithmic designers concerned with linear and nonlinear combinatorial optimization will find this volume...

In this paper we develop a new approach for studying overlapping iterated function systems. This approach is inspired by a famous result due to Khintchine from Diophantine approximation which shows that for a family of limsup sets, their Lebesgue measure...

Apologies but we at Booksplease don't have a full description for this book.About the AuthorRafael von Kanel, IAS Tsinghua University, Beijing, China.Book InformationISBN 9781470464165Author Rafael von KanelFormat PaperbackPage Count 142Imprint American...

This volume contains the proceedings of the Barcelona-Boston-Tokyo Number Theory Seminar, which was held in memory of Fumiyuki Momose, a distinguished number theorist from Chuo University in Tokyo.Momose, who was a student of Yasutaka Ihara, made...

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Number Theory Revealed: A Masterclass acquaints enthusiastic students with the ""Queen of Mathematics''. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like...

This book explores one of humanity's most profound intellectual journeys — the creation of numbers themselves. Moving beyond a simple chronological history of mathematics, this book examines the ideas and cultural contexts that gave rise to new kinds of...

Apologies but we at Booksplease don't have a full description for this book.Book InformationISBN 9781418169824Author Edmund LandauFormat HardbackPage Count 588Imprint Scholarly Publishing Office, University of Michigan LibraryPublisher Michigan...

Apologies but we at Booksplease don't have a full description for this book.Book InformationISBN 9781418167974Author Edmund LandauFormat HardbackPage Count 412Imprint Scholarly Publishing Office, University of Michigan LibraryPublisher Michigan...

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Apologies but we at Booksplease don't have a full description for this book.Book InformationISBN 9781418185596Author Edmund LandauFormat PaperbackPage Count 584Imprint Scholarly Publishing Office, University of Michigan LibraryPublisher Michigan...

Apologies but we at Booksplease don't have a full description for this book.Book InformationISBN 9781418186050Author Peter Gustav LeJeune DirichletFormat PaperbackPage Count 660Imprint Scholarly Publishing Office, University of Michigan LibraryPublisher...

This is a book for an undergraduate number theory course, senior thesis work, graduate level study, or for those wishing to learn about applications of number theory to data encryption and security. With no abstract algebra background required, it covers...

This book is summarizing the results of the workshop "Uniform Distribution and Quasi-Monte Carlo Methods" of the RICAM Special Semester on "Applications of Algebra and Number Theory" in October 2013. The survey articles in this book focus on number...

Paul Turan, one of the greatest Hungarian mathematicians, was born 100 years ago, on August 18, 1910. To celebrate this occasion the Hungarian Academy of Sciences, the Alfred Renyi Institute of Mathematics, the Janos Bolyai Mathematical Society and the...

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Famous Functions in Number Theory is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book...

Modular forms and Jacobi forms play a central role in many areas of mathematics. Over the last 10-15 years, this theory has been extended to certain non-holomorphic functions, the so-called ""harmonic Maass forms"". The first glimpses of this theory...