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COMPLEX NUMBERS

LATTICE SIMULATION AND ZETA FUNCTION APPLICATIONS


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Sinopse

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 numbers Includes historical anecdotes, ideas for further research, outlines of theory and a detailed analysis of the Riemann hypothesis Bridges any gaps that might exist between the two worlds of lattice sums and number theory

Detalhes do Produto

    • Ano de Edição: 2007
    • Ano:  2007
    • País de Produção: United States
    • Código de Barras:  2000836318810
    • ISBN:  9780857099426

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