2 citations · 6 across the 37 of their papers we have counts for
38 papers
Estimating the tail of the singular product for the Hardy Littlewood and Bateman Horn conjectures
Victor Volfson
This paper investigates the asymptotic behavior of the tail of the singular product arising in the Hardy Littlewood and Bateman Horn conjectures for one dimensional systems of poly…
Some questions of connection between summation functions and the corresponding Dirichlet series
Victor Volfson
The paper proves a generalization of Wintner's theorem on the asymptotics of summation functions to the case of summation functions with nonlinear asymptotics. The class of arithme…
An approach to determining the existence of a limit distribution of additive arithmetic functions
Victor Volfson
An approach will be proposed to determine the existence of a limit distribution of additive arithmetic functions in this work. It is based on assertions that will be proven in this…
Summation functions with nonlinear asymptotic behavior
Victor Volfson
The paper considers a universal approach that allows one to quite simply obtain nonlinear asymptotic estimates of various summation functions. It is shown the application of this a…
Asymptotic behavior of summation functions from bounded arithmetic multiplicative functions
Victor Volfson
The paper considers estimates for the asymptotics of summation functions of bounded multiplicative arithmetic functions. Several assertions on this subject are proved and examples…
Extremal estimates for strongly additive and strongly multiplicative arithmetic functions
Victor Volfson
The paper considers estimates for some sums and products of functions of prime numbers. Several assertions on this topic have been proven. We also study extremal estimates for stro…
Maximum distance between consecutive primes and other related questions
Victor Volfson
The paper considers the asymptotic of the ratio of the number of primes not exceeding the primorial and the number of residues in the reduced system of residues for the given primo…
Estimation of the asymptotic behavior of summation functions
Victor Volfson
The paper considers asymptotics of summation functions of additive and multiplicative arithmetic functions. We also study asymptotics of summation functions of natural and prime ar…
Asymptotic behavior "almost everywhere" of additive and multiplicative arithmetic functions
Victor Volfson
We define the asymptotic behavior "almost everywhere" of additive and multiplicative arithmetic functions in the paper. Classes of additive and multiplicative arithmetic functions…
Asymptotics of the number of primes and sums of functions of primes in a subset of natural series
Victor Volfson
The paper solves the problems of determining the asymptotics of the number of primes and the sums of functions of primes in a subset of the natural series that satisfies the condit…
Asymptotics of sums of functions of primes located on an arithmetic progression
Victor Volfson
We investigate the problem of the distribution of sums of functions of prime numbers located on an arithmetic progression. This problem is closely related to the problem of the dis…
Asymptotics of probability characteristics of additive arithmetic functions
Victor Volfson
We study the questions of determining the asymptotics of the probabilistic characteristics of additive arithmetic functions in the paper, regardless of whether they have a limit di…
An estimate of asymptotics of the moments of additive arithmetic functions with a limit distribution defined on a subset of the natural series
Victor Volfson
We study the asymptotics of the moments of arithmetic functions that have a limit distribution, not necessarily normal, defined on a subset of the natural series that satisfies cer…
Additive arithmetic functions with limit normal distribution
Victor Volfson
This paper proves several assertions on sufficient conditions for the convergence of additive arithmetic functions to the normal distribution. A generalization of the Erdos-Kac the…
Determination of the asymptotic behavior of probabilistic characteristics of arithmetic functions and some other questions of probabilistic number theory
Victor Volfson
One of the questions of distribution of prime numbers is considered in the article. It is shown what error is obtained from the assumption that the asymptotic density of a sequence…
Asymptotics for sums of functions of primes
Victor Volfson
This work gives a general approach to the determination of the asymptotic behavior of the sums of functions of primes based on the distribution of primes. It refines the estimate o…
Asymptotic of summation functions
Victor Volfson
We will study the asymptotic behavior of summation functions of a natural argument, including the asymptotic behavior of summation functions of a prime argument in the paper. A gen…
Asymptotic of the greatest distance between adjacent primes and the Hardy-Littlewood conjecture
Victor Volfson
The paper substantiates the conjecture of the asymptotic behavior of the largest distance between consecutive primes: , where…
Determination of the asymptotic behavior of the number of natural solutions for certain types of diagonal Diophantine equations
Victor Volfson
We obtain asymptotic upper bounds for the number of natural solutions of the following diagonal Diophantine equations in a hypercube with side - in the paper: $x_1 = x_2^k+...+…
Summation arithmetic functions with bounded terms, having a limit normal distribution law
Victor Volfson
The paper considers the properties of pseudo stationarity in a broad sense and pseudo strong mixing for sequences of random variables corresponding to arithmetic functions. Asserti…
Asymptotic of summation arithmetic functions, the limit for which is the law of normal distribution
Victor Volfson
Summation arithmetic functions with asymptotically independent terms are studied in the paper, the limit of which is the law of normal distribution. Assertions about the asymptotic…
Asymptotic of some sums
Victor Leonidovich Volfson
The paper compares the asymptotic of the expressions and , $\frac {1} {x} \sum\limits_{p \l…
Summation arithmetic functions with asymptotically independent summands
Victor Volfson
The summation arithmetic functions with asymptotically independent summands are studied in the paper. We prove statements about the condition under which the summation arithmetic f…
Investigations of Mertens and Liouville summation functions
Victor Volfson
Summation arithmetic functions of Mertens and Liouville are investigated in the paper. It is proved that the limiting distribution of these functions is the normal. It is also show…