Focusing on the solution of Diophantine equations, this graduate-level textbook delves into equations that require integer, rational, or algebraic number solutions. It emphasizes the significance of these equations in the context of modern arithmetic algebraic geometry. The text explores this central theme through three distinct aspects, providing a comprehensive understanding of the interplay between number theory and algebraic geometry.
Henri Cohen Libri






Focusing on the solution of Diophantine equations, this book delves into the methods and techniques for solving polynomial equations that require integer, rational, or algebraic number solutions. It explores the intricacies of these equations and provides insights into their mathematical significance and applications.
Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects.
A course in computational algebraic number theory
- 545pagine
- 20 ore di lettura
A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.
Focusing on explicit number theory, this book explores the solution of Diophantine equations through a comprehensive collection of topics. It features over 350 exercises that reinforce the concepts presented, making it accessible and engaging for readers. The text is largely self-contained, allowing for a thorough understanding of the material without requiring extensive prior knowledge.
Focusing on the resolution of Diophantine equations, this book delves into the techniques and methodologies for solving polynomial equations that require integer, rational, or algebraic number solutions. It explores various approaches and theories related to these equations, highlighting their significance in number theory and mathematics as a whole.
Algorithmic number theory
- 405pagine
- 15 ore di lettura
This book constitutes the refereed post-conference proceedings of the Second International Algorithmic Number Theory Symposium, ANTS-II, held in Talence, France in May 1996. The 35 revised full papers included in the book were selected from a variety of submissions. They cover a broad spectrum of topics and report state-of-the-art research results in computational number theory and complexity theory. Among the issues addressed are number fields computation, Abelian varieties, factoring algorithms, finite fields, elliptic curves, algorithm complexity, lattice theory, and coding.