| Description |
1 online resource (xii, 131 pages) : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Bibliography |
Includes bibliographical references and index. |
| Note |
Print version record. |
| Summary |
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. |
| Subject |
Numbers, Complex.
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Lattice theory.
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Functions, Zeta.
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Nombres complexes.
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Théorie des treillis.
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Fonctions zêta.
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MATHEMATICS -- Algebra -- Intermediate.
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Functions, Zeta
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Lattice theory
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Numbers, Complex
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| Other Form: |
Print version: Roy, Stephen C. (Stephen Campbell). Complex numbers 1904275257 (DLC) 2007390295 (OCoLC)77661440 |
| ISBN |
9780857099426 (electronic bk.) |
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0857099426 (electronic bk.) |
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1904275257 |
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9781904275251 |
| Standard No. |
AU@ 000056890174 |
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CHNEW 001011800 |
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DEBBG BV042317156 |
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DEBSZ 414270800 |
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GBVCP 813168511 |
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