Vigtor Volfson
Published 2016-08-11Version 1
This paper investigates the upper bound of the number of integer (natural) solutions of inhomogeneous algebraic Diophantine diagonal equations with integer coefficients without a free member via the circle method of Hardy and Littlewood. Author found the upper bound of the number of natural solutions of inhomogeneous algebraic Diophantine diagonal equations with explicit variable. He developed a method in the paper, which allows you to perform the low estimate of the number of natural (integer) solutions of algebraic Diophantine equation with integer coefficients. Author obtained a lower estimate (with this method) of the number of integer (natural) solutions for certain kinds of inhomogeneous algebraic Diophantine diagonal equations with integer coefficients with any number of variables (including Thue equation).
Comments: 16 pages. arXiv admin note: text overlap with arXiv:1604.07646
Estimations of the number of solutions of algebraic Diophantine equations with natural coefficients using the circle method of Hardy-Littlewood
Integer conversions and estimation of the number of integer solutions of algebraic Diophantine equations
Systems of cubic forms in many variables
![QR code for arXiv:1608.03459 [math.NT]](http://oss.arxitics.com/images/favicon.svg)