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License Agreement on scientific materials use.
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STUDY OF NON-TRIVIAL ZEROS OF RIEMANN ZETA-FUNCTION
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Vadim Nikolaevich Romanov
Saint Petersburg
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Submitted:
June 1, 2015
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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.
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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
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