Predrag B. Petrović – författare

The Riemann zeta function plays a central role in many areas in which complex analysis is applied, such as number theory (e.g. generating irrational and prime numbers. It is also an important tool in signal analysis in many fields of contemporary practice and technology, cryptography. In condensed matter physics, for example, the famous Sommerfeld expansion, which is used to calculate the number of particles and the internal electron energy, includes the Riemann zeta function with even integer argument values. On the other hand, the spin-spin correlation function of isotropic spin-1/2 in the Heisenberg model is expressed by ln 2 and Riemann zeta function with odd integer arguments. The author has made a tremendous effort to provide the reader with a new, clear and innovative way of looking at the most important features of the Riemann zeta function. The proofs of the expressed theorems are completely original. The monography established a good theoretical basis for the problem of calculating multiple sums and integrals in which the Riemann function appears. A special method was developed to establish a connection between the values of the Riemann zeta function with odd and even integer arguments. Based on the results obtained by H. M. Srivastava in his study from 1988, related to several different groups of summation formulas with the series in which the Riemann zeta function appears (which was first investigated by Euler and Goldbach), the monograph dealt with the series of this type. A new formula will be offered for Riemann function for odd argument which has a more compact form and faster convergence than any of the relations described in the afore mentioned papers.

In real electronic systems, voltage and current signals are not necessarily of a periodical quantity, due to the presence of nonharmonic components or/and possible stochastic variation. This book presents in three parts methods for analyzing and processing and reconstructing complex signals.The first part of this book is dedicated to the problem of measurements of the basic electric quantities in electric utilities, both from the aspect of accuracy of this type of measurements and the possibilities of simple and practical realization. The second part presents a reconstruction of trigonometric polynomials, a specific class of band-limited signals, from a number of integrated values of input signals. The third part deals with the problem of estimating the value of the active power of the ac signal in the presence of subharmonics and interharmonics. The analysis makes use of the most general model of the voltage and current signal, i.e. the most complex spectral content that can be expected to appear in practice.