Table of Contents

Dedication
About our Author
Author’s Preface

Background
Important features
Acknowledgements
DEPENDENCE CHART


Notations
1. Introduction

1.1 COMPLEX NUMBERS
1.2 SCOPE OF THE TEXT
1.3 G. F. B. RIEMANN AND THE ZETA FUNCTION
1.4 STUDIES OF THE XI FUNCTION BY H. VON MANGOLDT
1.5 RECENT WORK ON THE ZETA FUNCTION
1.6 P. P. EWALD AND LATTICE SUMMATION


2. Theory

2.1 COMPLEX NUMBER ARITHMETIC
2.2 ARGAND DIAGRAMS
2.3 EULER IDENTITIES
2.4 POWERS AND LOGARITHMS
2.5 THE HYPERBOLIC FUNCTION
2.6 INTEGRATION PROCEDURES USED IN CHAPTERS 3 & 4
2.7 STANDARD INTEGRATION WITH COMPLEX NUMBERS
2.8 LINE AND CONTOUR INTEGRATION


3. The Riemann Zeta Function

3.1 INTRODUCTION
3.2 THE FUNCTIONAL EQUATION
3.3 CONTOUR INTEGRATION PROCEDURES LEADING TO N(T)
3.4 A NEW STRATEGY FOR THE EVALUATION OF N(T) BASED ON VON MANGOLDT’S METHOD
3.5 COMPUTATIONAL EXAMINATION OF ζ(s)
3.6 CONCLUSION AND FURTHER WORK


4. Ewald Lattice Summation

4.1 COMPUTER SIMULATION OF IONIC SOLIDS
4.2 CONVERGENCE OF LATTICE WAVES WITH ATOMIC POSITION
4.3 VECTOR POTENTIAL CONVERGENCE WITH ATOMIC POSITION
4.4 DISCUSSION AND FINAL ANALYSIS OF THE EWALD METHOD
4.5 CONCLUSION AND FURTHER WORK
APPENDIX 1
APPENDIX 2


Bibliography
Glossary
Index

About the Author

Dr. Stephen Campbell Roy from the green and pleasant Scottish town of Maybole in Ayreshire, received his secondary education at the Carrick Academy, and then studied chemistry at Heriot-Watt University, Edinburgh where he was awarded a BSc (Hons.) in 1991. Moving to St Andrews University, Fife he studied electro-chemistry and in 1994 was awarded his PhD. He then moved to Newcastle University for work in postdoctoral research until 1997. Then to Manchester University as a temporary Lecturer in Chemistry to teach electrochemistry and computer modelling to undergraduates.

Reviews

The reader will not be disappointed., Zentralblatt MATH
Roy applies his expertise both in the subject and in teaching in this digestible treatment., SciTech News
Offers a fresh and critical approach to research-based implementation of the mathematical concept of imaginary numbers., Mathematical Reviews