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Numerical Algorithms for Number Theory - Using Pari/GP (Paperback)
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Numerical Algorithms for Number Theory - Using Pari/GP (Paperback)
Series: Mathematical Surveys and Monographs
Expected to ship within 12 - 17 working days
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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
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.
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