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Complex numbers : lattice simulation and zeta function applications /
An informative and useful account of complex numbers that includes historical anecdotes, ideas for further research, outlines of theory and a detailed analysis of the ever-elusory Riemann hypothesis. Stephen Roy assumes no detailed mathematical knowledge on the part of the reader and provides a fasc...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Chichester :
Horwood,
2007.
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| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | An informative and useful account of complex numbers that includes historical anecdotes, ideas for further research, outlines of theory and a detailed analysis of the ever-elusory Riemann hypothesis. Stephen Roy assumes no detailed mathematical knowledge on the part of the reader and provides a fascinating description of the use of this fundamental idea within the two subject areas of lattice simulation and number theory. Complex Numbers offers a fresh and critical approach to research-based implementation of the mathematical concept of imaginary numbers. Detailed coverage includes:Riemann's zeta function: an investigation of the non-trivial roots by Euler-Maclaurin summation. Basic theory: logarithms, indices, arithmetic and integration procedures are described. Lattice simulation: the role of complex numbers in Paul Ewald's important work of the I 920s is analysed. Mangoldt's study of the xi function: close attention is given to the derivation of N(T) formulae by contour integration. Analytical calculations: used extensively to illustrate important theoretical aspects. Glossary: over 80 terms included in the text are defined. Offers a fresh and critical approach to the research-based implication of complex numbersIncludes historical anecdotes, ideas for further research, outlines of theory and a detailed analysis of the Riemann hypothesisBridges any gaps that might exist between the two worlds of lattice sums and number theory. |
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| Descripción Física: | 1 online resource (xii, 131 pages) : illustrations |
| Bibliografía: | Includes bibliographical references and index. |
| ISBN: | 9780857099426 0857099426 |