Number theory

This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable.

The book attempts to point out the interconnections between number theory and algebra with a view to making a student understand certain basic concepts in the two areas forming the subject-matter of the book.

The book attempts to point out the interconnections between number theory and algebra with a view to making a student understand certain basic concepts in the two areas forming the subject-matter of the book.

A detailed and self-contained introduction to a key part of local number theory, ideal for graduate students and researchers.

A detailed and self-contained introduction to a key part of local number theory, ideal for graduate students and researchers.

A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.

A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.

A comprehensive, graduate-level treatment of unit equations and their various applications.

This book leads readers from simple number work to the point where they can prove the classical results of elementary number theory for themselves.

A graduate text providing a brisk, thorough treatment of the foundations of algebraic number theory.

This is a modern introduction to the analytic techniques used in the investigation of zeta functions through the example of the Riemann zeta function.

This book is devoted to efficient pairing computations and implementations, useful tools for cryptographers working on topics like identity-based cryptography and the simplification of existing protocols like signature schemes.

Through three editions, Cryptography: Theory and Practice, has been embraced by instructors and students alike.

Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory.

Elementary Number Theory, 6th Edition, blends classical theory with modern applications and is notable for its outstanding exercise sets.

Classical number theory is developed from scratch leading to geometric discrepancy theory, with Fourier analysis introduced along the way.

This introductory text covers a variety of applications to interest every reader, from researchers to amateur mathematicians.

Classical number theory is developed from scratch leading to geometric discrepancy theory, with Fourier analysis introduced along the way.

This book provides a foundation for arithmetic topology, a new branch of mathematics that investigates the analogies between the topology of knots, 3-manifolds, and the arithmetic of number fields.

This book is unique in that its stress is not on the mastery of a programming language, but on the importance and value of interactive problem solving.

A highly successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming.

A highly successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming.

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.

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.

Praise for the First Edition beautiful and well worth the reading with many exercises and a good bibliography, this book will fascinate both students and teachers.

Praise for the First Edition beautiful and well worth the reading with many exercises and a good bibliography, this book will fascinate both students and teachers.

An exciting approach to the history and mathematics of number theory .

The only book to provide a unified view of the interplay between computational number theory and cryptography Computational number theory and modern cryptography are two of the most important and fundamental research fields in information security.

A complete, self-contained introduction to a powerful and resurging mathematical discipline Combinatorial Geometry presents and explains with complete proofs some of the most important results and methods of this relatively young mathematical discipline, started by Minkowski, Fejes T th, Rogers, and Erd's.

A unique synthesis of the three existing Fourier-analytic treatments of quadratic reciprocity.

The first comprehensive review of the theory and practice of one oftoday's most powerful optimization techniques.

This book provides a self-contained proof of the Mordell conjecture (Faltings''s theorem) and a concise introduction to Diophantine geometry.

Build a solid foundation in the area of arithmetic groups and explore its inherent geometric and number-theoretical components.

This introductory textbook for graduate students presents modern developments in probabilistic number theory, many for the first time.

A friendly and concise introduction to the Mahler measure – a fascinating subject in contemporary mathematics.

This introductory textbook for graduate students presents modern developments in probabilistic number theory, many for the first time.

A mathematical record of bounded prime gaps breakthroughs, from Erdős to Polymath8, with linked computer programs and complete appendices.

A mathematical record of bounded prime gaps breakthroughs, from Erdős to Polymath8, with linked computer programs and complete appendices.

A guide to cryptanalysis and the implementation of cryptosystems, written for students and security engineers by leading experts.

This volume contains research papers in mathematical logic, particularly in model theory and its applications to algebra and formal theories of arithmetic.

Volume 2 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.

Introduction to Diophantine approximation and equations focusing on Schmidt''s subspace theorem, with applications to transcendence.

A concise and comprehensive introduction to trace formula methods in the study of Shimura varieties and associated Galois representations.

A concise and comprehensive introduction to trace formula methods in the study of Shimura varieties and associated Galois representations.

Discover how zeta and L-functions have shaped the development of major parts of mathematics over the past two centuries.

Discover how zeta and L-functions have shaped the development of major parts of mathematics over the past two centuries.

A self-contained exposition of local class field theory for students in advanced algebra.

A self-contained exposition of local class field theory for students in advanced algebra.