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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… Read more
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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.
SR