SoftcoverISBN:  9781470463519 
Product Code:  SURV/254 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBookISBN:  9781470465568 
Product Code:  SURV/254.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
SoftcoverISBN:  9781470463519 
eBookISBN:  9781470465568 
Product Code:  SURV/254.B 
List Price:  $250.00$187.50 
MAA Member Price:  $225.00$168.75 
AMS Member Price:  $200.00$150.00 
Softcover ISBN:  9781470463519 
Product Code:  SURV/254 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470465568 
Product Code:  SURV/254.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470463519 
eBookISBN:  9781470465568 
Product Code:  SURV/254.B 
List Price:  $250.00$187.50 
MAA Member Price:  $225.00$168.75 
AMS Member Price:  $200.00$150.00 

Book DetailsMathematical Surveys and MonographsVolume: 254; 2021; 429 ppMSC: 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 RiemannSiegel 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 doublyexponential integration, EulerMacLaurin, AbelPlana, 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.ReadershipGraduate students and researchers interested in high precision numerical computations in number theory.

Table of Contents

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


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This book presents multiprecision algorithms used in number theory and elsewhere, such as extrapolation, numerical integration, numerical summation (including multiple zeta values and the RiemannSiegel 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 doublyexponential integration, EulerMacLaurin, AbelPlana, 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