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Author: Karim Belabas Publisher: American Mathematical Soc. ISBN: 1470463512 Category : Education Languages : en Pages : 429
Book Description
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 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.
Author: Karim Belabas Publisher: American Mathematical Soc. ISBN: 1470463512 Category : Education Languages : en Pages : 429
Book Description
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 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.
Author: Jonathan M. Borwein Publisher: Wiley-Interscience ISBN: Category : Computers Languages : en Pages : 472
Book Description
This book presents new research revealing the interplay between classical analysis and modern computation and complexity theory. Two intimately interwoven threads run through the text: the arithmetic-geometric mean (AGM) iteration of Gauss, Lagrange, and Legendre and the calculation of pi.
Author: Song Y Yan Publisher: World Scientific ISBN: 9814498270 Category : Mathematics Languages : en Pages : 360
Book Description
This book is about perfect, amicable and sociable numbers, with an emphasis on amicable numbers, from both a mathematical and particularly a computational point of view. Perfect and amicable numbers have been studied since antiquity, nevertheless, many problems still remain. The book introduces the basic concepts and results of perfect, amicable and sociable numbers and reviews the long history of the search for these numbers. It examines various methods, both numerical and algebraic, of generating these numbers, and also includes a set of important and interesting open problems in the area. The book is self-contained, and accessible to researchers, students, and even amateurs in mathematics and computing science. The only prerequisites are some familiarity with high-school algebra and basic computing techniques.
Author: Florian Hess Publisher: Springer ISBN: 354036076X Category : Mathematics Languages : en Pages : 609
Book Description
This book constitutes the refereed proceedings of the 7th International Algorithmic Number Theory Symposium, ANTS 2006, held in Berlin, July 2006. The book presents 37 revised full papers together with 4 invited papers selected for inclusion. The papers are organized in topical sections on algebraic number theory, analytic and elementary number theory, lattices, curves and varieties over fields of characteristic zero, curves over finite fields and applications, and discrete logarithms.
Author: Fernando Rodriguez Villegas Publisher: OUP Oxford ISBN: 0191523739 Category : Mathematics Languages : en Pages : 232
Book Description
This graduate text, based on years of teaching experience, is intended for first or second year graduate students in pure mathematics. The main goal of the text is to show how the computer can be used as a tool for research in number theory through numerical experimentation. The book contains many examples of experiments in binary quadratic forms, zeta functions of varieties over finite fields, elementary class field theory, elliptic units, modular forms, along with exercises and selected solutions. Sample programs are written in GP, the scripting language for the computational package PARI, and are available for download from the author's website.
Author: Abhijit Das Publisher: CRC Press ISBN: 1482205823 Category : Computers Languages : en Pages : 614
Book Description
Developed from the author's popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and pract
Author: Joachim von zur Gathen Publisher: Springer Science & Business Media ISBN: 3540694986 Category : Computers Languages : en Pages : 214
Book Description
This book constitutes the refereed proceedings of the Second International Workshop on the Arithmetic of Finite Fields, WAIFI 2008, held in Siena, Italy, in July 2008. The 16 revised full papers presented were carefully reviewed and selected from 34 submissions. The papers are organized in topical sections on structures in finite fields, efficient finite field arithmetic, efficient implementation and architectures, classification and construction of mappings over finite fields, and codes and cryptography.
Author: Karim Belabas
Author: Karim Belabas
Author: Jonathan M. Borwein
Author: Song Y Yan
Author: Luogeng Hua
Author: J. P. Buhler
Author: Florian Hess
Author: H. W. Lenstra
Author: Fernando Rodriguez Villegas
Author: Abhijit Das
Author: Joachim von zur Gathen