Complex Numbers: Lattice Simulation and Zeta Function Applications
by Stephen C Roy (9781904275251)

Complex Numbers: Lattice Simulation and Zeta Function Applications
 
Stephen C Roy
Release Date: 01 January 2007
Format: Paperback
Pages: 144
Category: Number Theory
Publisher: Horwood Publishing Limited
ISBN: 9781904275251
ISBN-10: 1904275257



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.

AUD $114.95

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