Complex numbers: lattice simulation and zeta function applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Chichester
Horwood
2007
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Includes bibliographical references and index 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 |
| Beschreibung: | 1 Online-Ressource (xii, 131 pages) |
| ISBN: | 9780857099426 0857099426 1904275257 9781904275251 |
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| 500 | |a Includes bibliographical references and index | ||
| 500 | |a 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 | ||
| 650 | 4 | |a Nombres complexes | |
| 650 | 4 | |a Treillis, Théorie des | |
| 650 | 4 | |a Fonctions zêta | |
| 650 | 7 | |a Functions, Zeta |2 fast | |
| 650 | 7 | |a Lattice theory |2 fast | |
| 650 | 7 | |a Numbers, Complex |2 fast | |
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| 650 | 4 | |a Lattice theory | |
| 650 | 4 | |a Functions, Zeta | |
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Datensatz im Suchindex
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| author | Roy, Stephen C., (Stephen Campbell) |
| author_facet | Roy, Stephen C., (Stephen Campbell) |
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| author_sort | Roy, Stephen C., (Stephen Campbell) |
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| building | Verbundindex |
| bvnumber | BV042317156 |
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| ctrlnum | (OCoLC)869282228 (DE-599)BVBBV042317156 |
| dewey-full | 512.788 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.788 |
| dewey-search | 512.788 |
| dewey-sort | 3512.788 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV042317156 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:18:16Z |
| institution | BVB |
| isbn | 9780857099426 0857099426 1904275257 9781904275251 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027754147 |
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| physical | 1 Online-Ressource (xii, 131 pages) |
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| spelling | Roy, Stephen C., (Stephen Campbell) Verfasser aut Complex numbers lattice simulation and zeta function applications Stephen C. Roy Chichester Horwood 2007 1 Online-Ressource (xii, 131 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references and index 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 Nombres complexes Treillis, Théorie des Fonctions zêta Functions, Zeta fast Lattice theory fast Numbers, Complex fast MATHEMATICS / Algebra / Intermediate bisacsh Numbers, Complex Lattice theory Functions, Zeta http://www.sciencedirect.com/science/book/9781904275251 Verlag Volltext |
| spellingShingle | Roy, Stephen C., (Stephen Campbell) Complex numbers lattice simulation and zeta function applications Nombres complexes Treillis, Théorie des Fonctions zêta Functions, Zeta fast Lattice theory fast Numbers, Complex fast MATHEMATICS / Algebra / Intermediate bisacsh Numbers, Complex Lattice theory Functions, Zeta |
| title | Complex numbers lattice simulation and zeta function applications |
| title_auth | Complex numbers lattice simulation and zeta function applications |
| title_exact_search | Complex numbers lattice simulation and zeta function applications |
| title_full | Complex numbers lattice simulation and zeta function applications Stephen C. Roy |
| title_fullStr | Complex numbers lattice simulation and zeta function applications Stephen C. Roy |
| title_full_unstemmed | Complex numbers lattice simulation and zeta function applications Stephen C. Roy |
| title_short | Complex numbers |
| title_sort | complex numbers lattice simulation and zeta function applications |
| title_sub | lattice simulation and zeta function applications |
| topic | Nombres complexes Treillis, Théorie des Fonctions zêta Functions, Zeta fast Lattice theory fast Numbers, Complex fast MATHEMATICS / Algebra / Intermediate bisacsh Numbers, Complex Lattice theory Functions, Zeta |
| topic_facet | Nombres complexes Treillis, Théorie des Fonctions zêta Functions, Zeta Lattice theory Numbers, Complex MATHEMATICS / Algebra / Intermediate |
| url | http://www.sciencedirect.com/science/book/9781904275251 |
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