Number Theory

This book deals with the development of Diophantine problems starting with Thue's path breaking result and culminating in Roth's theorem with applications. It discusses classical results including Hermite-Lindemann-Weierstrass theorem, Gelfond-Schneider...

This book contains 50 papers from among the 95 papers presented at the Seventh International Conference on Fibonacci Numbers and Their Applications which was held at the Institut Fiir Mathematik, Technische Universitiit Graz, Steyrergasse 30, A-SOlO...

Carl Ludwig Siegel gave a course of lectures on the Geometry of Numbers at New York University during the academic year 1945-46, when there were hardly any books on the subject other than Minkowski's original one. This volume stems from Siegel's...

It is an historical goal of algebraic number theory to relate all algebraic extensionsofanumber?eldinauniquewaytostructuresthatareexclusively described in terms of the base ?eld. Suitable structures are the prime ideals of the ring of integers of the...

Pell's Equation is a very simple Diophantine equation that has been known to mathematicians for over 2000 years. Even today research involving this equation continues to be very active, as can be seen by the publication of at least 150 articles related...

This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely...

From the Preface by H. Halberstam: "The unexpected arrival of Loo-Keng Hua in Europe in the fall of 1978 was for many of us a romantic event, a legend come to life. What had long been (and had seemed destined to remain) merely a revered name in the...

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This volume collects lecture notes and research articles from the International Autumn School on Computational Number Theory, which was held at the Izmir Institute of Technology from October 30th to November 3rd, 2017 in Izmir, Turkey. Written by experts...

By focusing on quadratic numbers, this advanced undergraduate or master's level textbook on algebraic number theory is accessible even to students who have yet to learn Galois theory. The techniques of elementary arithmetic, ring theory and linear...

This volume presents research and expository papers highlighting the vibrant and fascinating study of irregularities in the distribution of primes. Written by an international group of experts, contributions present a self-contained yet unified...

In the 1970s Hirzebruch and Zagier produced elliptic modular forms with coefficients in the homology of a Hilbert modular surface. They then computed the Fourier coefficients of these forms in terms of period integrals and L-functions. In this book the...

The main theme of this book is the theory of heights as they appear in various guises. This includes a large body of results on Mahlers measure of the height of a polynomial. The authors'approach is very down to earth as they cover the rationals,...

THIS volume is concerned with a substantial branch of number theory of which no connected account appears to exist; we describe the general nature of the constituent topics in the introduction. Although some excellent surveys dealing with limited aspects...

Apologies but we at Booksplease don't have a full description for this book.Springer Book ArchivesBook InformationISBN 9781461257905Author Catherine GoldsteinFormat PaperbackPage Count 366Imprint Springer-Verlag New York Inc.Publisher Springer-Verlag New...

This textbook is intended to serve as a one-semester introductory course in number theory and in this second edition it has been revised throughout and many new exercises have been added. Historical perspective is included and emphasis is given to some...

Algebraic numbers can approximate and classify any real number. Here, the author gathers together results about such approximations and classifications. Written for a broad audience, the book is accessible and self-contained, with complete and detailed...

The first of two companion volumes on anabelian algebraic geometry, this book contains the famous, but hitherto unpublished manuscript 'Esquisse d'un Programme' (Sketch of a Program) by Alexander Grothendieck. This work, written in 1984, fourteen years...

The aim of this book is to characterize certain multiplicative and additive arithmetical functions by combining methods from number theory with some simple ideas from functional and harmonic analysis. The authors achieve this goal by considering...

This volume contains selected contributions from a very successful meeting on Number Theory and Dynamical Systems held at the University of York in 1987. There are close and surprising connections between number theory and dynamical systems. One emerged...

The papers in this volume, which were presented at the 1985 Australian Mathematical Society convention, survey recent work in Diophantine analysis. The contributors are leading mathematicians in the world, and their articles are state of the art...

Number theory is one of the oldest and most appealing areas of mathematics. Computation has always played a role in number theory, a role which has increased dramatically in the last 20 or 30 years, both because of the advent of modern computers, and...

Cohomology of Drinfeld Modular Varieties provides an introduction, in two volumes, both to this subject and to the Langlands correspondence for function fields. These varieties are the analogues for function fields of the Shimura varieties over number...

This book is an authoritative description of the various approaches to and methods in the theory of irregularities of distribution. The subject is primarily concerned with number theory, but also borders on combinatorics and probability theory. The work...

In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory, including the hitherto nebulous study of...

The Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the function is closely bound with automorphic forms and that many...

This book provides a comprehensive account of a key (and perhaps the most important) theory upon which the Taylor-Wiles proof of Fermat's last theorem is based. The book begins with an overview of the theory of automorphic forms on linear algebraic...

Nearly a hundred years have passed since Viggo Brun invented his famous sieve, and the use of sieve methods is constantly evolving. As probability and combinatorics have penetrated the fabric of mathematical activity, sieve methods have become more...

There is now much interplay between studies on logarithmic forms and deep aspects of arithmetic algebraic geometry. New light has been shed, for instance, on the famous conjectures of Tate and Shafarevich relating to abelian varieties and the associated...

In the late sixties Matiyasevich, building on the work of Davis, Putnam and Robinson, showed that there was no algorithm to determine whether a polynomial equation in several variables and with integer coefficients has integer solutions. Hilbert gave...

L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible...

In the past few years elliptic curve cryptography has moved from a fringe activity to a major challenger to the dominant RSA/DSA systems. Elliptic curves offer major advances on older systems such as increased speed, less memory and smaller key sizes. As...

The contributions in this book are based on the lectures delivered at the Seminaire de theorie des nombres de Paris during the academic year 93-94. It is the fifteenth annual volume. This book covers the whole spectrum of number theory, and is composed...

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...

Sieve theory has a rich and romantic history. The ancient question of whether there exist infinitely many twin primes (primes p such that p+2 is also prime), and Goldbach's conjecture that every even number can be written as the sum of two prime numbers,...

This volume has grown out of lectures given by Professor Pfister over many years. The emphasis here is placed on results about quadratic forms that give rise to interconnections between number theory, algebra, algebraic geometry and topology. Topics...

Many classical and modern results and quadratic forms are brought together in this book. The treatment is self-contained and of a totally elementary nature requiring only a basic knowledge of rings, fields, polynomials, and matrices, such that the works...

This introduction to recent work in p-adic analysis and number theory will make accessible to a relatively general audience the efforts of a number of mathematicians over the last five years. After reviewing the basics (the construction of p-adic numbers...

This book is a self-contained account of the theory of classgroups of group rings. The guiding philosophy has been to describe all the basic properties of such classgroups in terms of character functions. This point of view is due to A. Frohlich and it...

The theory of sets of multiples, a subject which lies at the intersection of analytic and probabilistic number theory, has seen much development since the publication of Sequences by Halberstam and Roth nearly thirty years ago. The area is rich in...