**Mathematical Surveys and Monographs**

Volume: 254;
2021;
429 pp;
Softcover

MSC: Primary 11; 65; 30;

**Print ISBN: 978-1-4704-6351-9
Product Code: SURV/254**

List Price: $125.00

AMS Member Price: $100.00

MAA Member Price: $112.50

**Electronic ISBN: 978-1-4704-6556-8
Product Code: SURV/254.E**

List Price: $125.00

AMS Member Price: $100.00

MAA Member Price: $112.50

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#### Supplemental Materials

# Numerical Algorithms for Number Theory: Using Pari/GP

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*Karim Belabas; Henri Cohen*

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.

#### Readership

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

#### Table of Contents

# Table of Contents

## Numerical Algorithms for Number Theory: Using Pari/GP

Table of Contents pages: 1 2

- Appendix A. List of relevant GP programs 426426
- Bibliography 428428
- Index of Programs 432432
- General Index 436436

Table of Contents pages: 1 2