Numerical Algorithms for Number Theory: Using Pari/GP

This book provides multiprecision algorithms for number theory and other fields, including extrapolation, numerical integration, summation, continued fractions, Euler products, inverse Mellin transforms, and complex $L$-functions. It offers detailed implementations in the Pari/GP system, making it valuable for anyone interested in number theory, practical implementations, computer experiments, and numerical algorithms with thousands of digits of accuracy.

Format: Paperback / softback
Length: 430 pages
Publication date: 01 July 2021
Publisher: American Mathematical Society

This comprehensive book delves into the realm of multiprecision algorithms, which find applications in various fields, including number theory and beyond. It presents a wide array of techniques and methods for solving complex mathematical problems with precision and accuracy.

The book begins by introducing the fundamental concepts and principles of multiprecision arithmetic, providing a solid foundation for the subsequent chapters. It then explores a range of applications, such as extrapolation, numerical integration, summation, and evaluation of continued fractions.

For each task, numerous algorithms are presented, each designed to achieve optimal performance. These algorithms encompass a diverse spectrum, including Gaussian and doubly-exponential integration, Euler-MacLaurin summation, Abel-Plana summation, Lagrange summation, and Monien summation. Each algorithm is thoroughly explained, accompanied by a comprehensive implementation in the free Pari/GP system.

The implementations not only enhance the understanding of the algorithms' inner workings but also serve as a gentle introduction to advanced features of the Pari/GP language. This dual purpose ensures that readers gain a deep appreciation for both the theoretical aspects and practical applications of multiprecision algorithms.

The book is particularly valuable to anyone with an interest in number theory, particularly in the areas of practical implementations, computer experiments, and numerical algorithms capable of producing thousands of digits of accuracy. It serves as a valuable resource for researchers, mathematicians, and practitioners seeking to advance their knowledge and expertise in this field.

In conclusion, this book is a must-read for anyone seeking to explore the realm of multiprecision algorithms and their applications in number theory and beyond. Its comprehensive coverage, detailed explanations, and practical implementations make it an invaluable resource for researchers, mathematicians, and practitioners alike.

Weight: 776g
Dimension: 180 x 255 x 25 (mm)
ISBN-13: 9781470463519