6 papers · 1 filter
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…
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…
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…
Contradictions in some primes conjectures
Victor Volfson
This paper demonstrates that from the Cramer's, Hardy-Littlewood's and Bateman-Horn's conjectures (suggest that the probability of a large positive integer being a prime - $\fr…