EN | RU    
Scientific & Technical Literature Publishing House
Search:

Home»

Contact Us»

Journals»

News»

Preparation of Papers»

Advertising»

Feedback»

Books»

About Us»



advertisement



Applied Physics and Mathematics

Annotation
<< Back
INVESTIGATION OF THE LIMIT DISTRIBUTION AND THE ASYMPTOTIC BEHAVIOR OF SUMMATION ARITHMETIC FUNCTIONS
V.L. VOLFSON

The problem of distribution of prime numbers has acquired an important practical signifi cance, since it is directly related to
the reliability of cryptographic systems with a public key. For example, the cryptographic resistance of the widely used RSA
encryption system is based on the computational complexity of prime factorization of large natural numbers. We investigate
arithmetic functions and, in particular, the distribution of the number of primes in the paper. The aim of this paper is to
study the limit distributions and the asymptotic behavior of summation arithmetic functions. A probabilistic approach is
used for these purposes, based on the use of the axioms of probability theory. Arithmetic functions of the number of natural
numbers possessing a certain property are considered. Suffi cient conditions are proved under which these functions have
a limiting normal distribution. Arithmetic functions of this type with a limiting normal distribution are shown. The author
investigates summation functions of a general form and fi nds suffi cient conditions under which they have a limiting normal
distribution. Examples of arithmetic functions that satisfy these requirements are considered. We prove an ergodic theorem
for summation arithmetic functions: where for which the sequence of random variables
xn has the stationarity property in the broad sense. An estimate is obtained for the standard deviation of the summation
arithmetic function from the mean value by elementary methods under similar conditions. The asymptotics of the growth
of the deviation of the values of the arithmetic function from its mean value are investigated. It is shown that an equivalent
formulation of the Riemann hypothesis for the Mertens function is satisfi ed almost everywhere.
Keywords: summation arithmetic function, Mertens function, probability space, sequence of random variables, stationarity
in a broad sense, limit distribution, normal distribution, ergodic theorem, asymptotics of growth of deviation from the mean
value.

Contacts: E-mail: znakvicvolf@mail.ru

Pp. 50-60.

 Sections

«About journal

«Archive

«Thematic focus of the journal

«Formatting rules

«Stages of the review and publication

«Review process

«Editorial and Professional Ethics

«Detecting plagiarism

«Editors and Editorial Board

«News journal


 Journals
...................................
Instruments and Systems: Monitoring, Control, and Diagnostics
...................................
Instrument-Making and Automation Means. Encyclopedic Textbook
...................................
Industrial Automatic Control Systems and Controllers
...................................
Ecological Systems and Devices
...................................
Aerospace Instrument-Making
...................................
Engineering Physics
...................................
History of Science and Engineering
...................................
Music and Time
...................................
Note Album
...................................
Musicology
...................................
Universal History
...................................
Directory of engineer
...................................
Applied Physics and Mathematics
...................................
News Academy of Engineering Sciences A.M. Prokhorov
...................................

Last news:

Выставки по автоматизации и электронике «ПТА-Урал 2018» и «Электроника-Урал 2018» состоятся в Екатеринбурге

Открыта электронная регистрация на выставку Дефектоскопия / NDT St. Petersburg

Открыта регистрация на 9-ю Международную научно-практическую конференцию «Строительство и ремонт скважин — 2018»

ExpoElectronica и ElectronTechExpo 2018: рост площади экспозиции на 19% и новые формы контент-программы

Тематика и состав экспозиции РЭП на выставке "ChipEXPO - 2018"

   Rambler's Top100 Rambler's Top100         


    Management system developed by: ananskikh.ru
© Publishing House "NAUCHTEKHLITIZDAT", 2005-2024