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Complex Numbers

Lattice Simulation and Zeta Function Applications

  • 1st Edition - July 1, 2007
  • Author: S C Roy
  • Language: English
  • eBook ISBN:
    9 7 8 - 0 - 8 5 7 0 9 - 9 4 2 - 6

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… Read more

Complex Numbers

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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.