Archive of Scientific Articles

Abstract. The article is devoted to the non-trivial zeros of Riemann zeta-function. The direct calculations of zeros positions at different argument values are carried out. The paper studies the behaviour and determines the position of the characteristic points (maxima, minima and zeros) of series approximating zeta-function. The article shows the invariance of zeros set with respect to symmetry transformations, namely, axial and central symmetry. On this basis a method of the proof of Riemann hypothesis is proposed. An interpretation of the hypothesis by the example of atomic system with certain symmetry properties of its wave function is given.

Key words and phrases: простые числа, сумма обратных степеней, дзета-функция Римана, гипотеза Римана, нетривиальные нули дзета-функции, функциональные соотношения для дзета-функции, преобразования симметрии, prime numbers, sum of inverse degrees, Riemann zeta-function, Riemann hypothesis, non-trivial zeros of zeta-function, functional ratios for zeta-function, symmetry transformations