GRAMOTA Publishers suggests publishing your scientific articles in periodicals
Pan-ArtPedagogy. Theory & PracticePhilology. Theory & PracticeManuscript

Archive of Scientific Articles

SOURCE:    Almanac of Modern Science and Education. Tambov: Gramota, 2015. № 6. P. 128-132.
SCIENTIFIC AREA:    Physical-Mathematical Sciences
Procedure of Scientific Articles Publication | To Show Issue Content | To Show All Articles in Section | Subject Index

License Agreement on scientific materials use.


Romanov Vadim Nikolaevich
Saint Petersburg

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
Open the whole article in PDF format. Free PDF-files viewer can be downloaded here.
  1. Gradshtein I. S., Ryzhik I. M. Tablitsy integralov, summ, ryadov i proizvedenii. M.: FML, 1962. 1100 s.
  2. Spravochnik po spetsial'nym funktsiyam / pod red. M. Abramovits, I. Stigan. M.: Nauka (FML), 1979. 832 s.
  3. Uitteker E. T., Vatson Dzh. N. Kurs sovremennogo analiza. M.: FML, 1963. Ch. 2. Transtsendentnye funktsii. 516 s.
  4. Yanke E., Emde F., Lesh F. Spetsial'nye funktsii. M.: Nauka (FML), 1968. 344 s.

Procedure of Scientific Articles Publication | To Show Issue Content | To Show All Articles in Section | Subject Index

© 2006-2024 GRAMOTA Publishers

site development and search engine optimization (seo):