7 papers
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+...+…
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…
Integer conversions and estimation of the number of integer solutions of algebraic Diophantine equations
Victor Volfson
The paper assesses the top number of integer solutions for algebraic Diophantine Thue diagonal equation of the degree and number of variables and equations with…
Estimating of the number of integer (natural) solutions of inhomogeneous algebraic Diophantine diagonal equations with integer coefficients
Victor Volfson
This paper investigates the upper bound of the number of integer (natural) solutions of inhomogeneous algebraic Diophantine diagonal equations with integer coefficients without a f…
Quantitative indicators of the solutions of Diophantine equations and systems in the domain of the natural numbers
Victor Volfson
The paper shows that the asymptotic density of solutions of Diophantine equations or systems of the natural numbers is 0. The author provides estimation methods and estimates numbe…