Complex Numbers. Lattice Simulation and Zeta Function Applications
This book contains a discussion of some interesting topics from applications of complex analysis to a discussion of the Riemann conjecture on a distribution of zeros of the Riemann zeta function and the Ewald lattice summation (used to calculate electrostatic potentials in crystal lattices). The book is clearly designed for non-specialists. It starts with a discussion of the most basic facts from complex analysis (it slowly introduces complex numbers, it describes some elementary functions in the complex domain and it touches on contour integration of complex functions and basic theorems of complex function theory). Many notions in complex analysis are defined in an unusual way (by illustrating them on some particularly simple examples without any attempt to present the precise definitions used in standard mathematical books). The main body of the book contains many tables of values of various functions in chosen finite sets of points as well as lots of graphical presentations of such tables. All of this is mixed with many quotations of various important papers and historical comments. It is a very unusual book.