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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…
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…
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…
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…