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OverviewThis 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. Full Product DetailsAuthor: Karim Belabas , Henri CohenPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.768kg ISBN: 9781470463519ISBN 10: 1470463512 Pages: 430 Publication Date: 30 August 2021 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction 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 Bibliography Index of programs General index.ReviewsAuthor InformationKarim Belabas, Universite de Bordeaux, France, and Henri Cohen, Universite de Bordeaux, France Tab Content 6Author Website:Countries AvailableAll regions |
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