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Numerical Algorithms for Number Theory: Using Pari/GP

Karim Belabas Université de Bordeaux, Bordeaux, France
Henri Cohen Université de Bordeaux, Bordeaux, France
Available Formats:
Softcover ISBN: 978-1-4704-6351-9
Product Code: SURV/254
List Price: $125.00 MAA Member Price:$112.50
AMS Member Price: $100.00 Electronic ISBN: 978-1-4704-6556-8 Product Code: SURV/254.E List Price:$125.00
MAA Member Price: $112.50 AMS Member Price:$100.00
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List Price: $187.50 MAA Member Price:$168.75
AMS Member Price: $150.00 Click above image for expanded view Numerical Algorithms for Number Theory: Using Pari/GP Karim Belabas Université de Bordeaux, Bordeaux, France Henri Cohen Université de Bordeaux, Bordeaux, France Available Formats:  Softcover ISBN: 978-1-4704-6351-9 Product Code: SURV/254  List Price:$125.00 MAA Member Price: $112.50 AMS Member Price:$100.00
 Electronic ISBN: 978-1-4704-6556-8 Product Code: SURV/254.E
 List Price: $125.00 MAA Member Price:$112.50 AMS Member Price: $100.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$187.50 MAA Member Price: $168.75 AMS Member Price:$150.00
• Book Details

Mathematical Surveys and Monographs
Volume: 2542021; 429 pp
MSC: Primary 11; 65; 30;

This book presents multiprecision algorithms used in number theory and elsewhere, such as extrapolation, numerical integration, numerical summation (including multiple zeta values and the Riemann-Siegel formula), evaluation and speed of convergence of continued fractions, Euler products and Euler sums, inverse Mellin transforms, and complex $L$-functions.

For each task, many algorithms are presented, such as Gaussian and doubly-exponential integration, Euler-MacLaurin, Abel-Plana, Lagrange, and Monien summation. Each algorithm is given in detail, together with a complete implementation in the free Pari/GP system. These implementations serve both to make even more precise the inner workings of the algorithms, and to gently introduce advanced features of the Pari/GP language.

This book will be appreciated by anyone interested in number theory, specifically in practical implementations, computer experiments and numerical algorithms that can be scaled to produce thousands of digits of accuracy.

Graduate students and researchers interested in high precision numerical computations in number theory.

• Chapters
• Introduction
• Numerical extrapolation
• Numerical integration
• Numerical summation
• Euler products and Euler sums
• Gauss and Jacobi sums
• Numerical computation of continued fractions
• Computation of inverse Mellin transforms
• Computation of $L$-functions
• List of relevant GP programs

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 2542021; 429 pp
MSC: Primary 11; 65; 30;

This book presents multiprecision algorithms used in number theory and elsewhere, such as extrapolation, numerical integration, numerical summation (including multiple zeta values and the Riemann-Siegel formula), evaluation and speed of convergence of continued fractions, Euler products and Euler sums, inverse Mellin transforms, and complex $L$-functions.

For each task, many algorithms are presented, such as Gaussian and doubly-exponential integration, Euler-MacLaurin, Abel-Plana, Lagrange, and Monien summation. Each algorithm is given in detail, together with a complete implementation in the free Pari/GP system. These implementations serve both to make even more precise the inner workings of the algorithms, and to gently introduce advanced features of the Pari/GP language.

This book will be appreciated by anyone interested in number theory, specifically in practical implementations, computer experiments and numerical algorithms that can be scaled to produce thousands of digits of accuracy.

Graduate students and researchers interested in high precision numerical computations in number theory.

• Chapters
• Introduction
• Numerical extrapolation
• Numerical integration
• Numerical summation
• Euler products and Euler sums
• Gauss and Jacobi sums
• Numerical computation of continued fractions
• Computation of inverse Mellin transforms
• Computation of $L$-functions
• List of relevant GP programs
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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