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- W4293482216 abstract "Author developed a method in the paper, which, unlike the circle method of Hardy and Littlewood (CM), allows you to perform a lower estimate for the number of natural (integer) solutions of algebraic Diophantine equation with integer coefficients. It was found the lower estimate of the number of natural solutions to various types of homogeneous algebraic Diophantine equations with integer coefficients diagonal form with any number of variables using this method. Author obtained upper bound of the number of the natural solutions (using CM) of one type of homogeneous Diophantine equation for values $k geq log_2 s$, where $k$ is the degree of the equation and $s$ is the number of variables. It was also found the upper bound of the number of the natural solutions of the homogeneous algebraic Diophantine equation with integer coefficients with a small number of variables. Author investigated the relations of upper and lower estimates of the number of natural solutions of homogeneous Diophantine equation with integer coefficients diagonal form in the paper." @default.
- W4293482216 created "2022-08-29" @default.
- W4293482216 creator A5061016995 @default.
- W4293482216 date "2016-04-26" @default.
- W4293482216 modified "2023-09-27" @default.
- W4293482216 title "Estimating of the number of natural solutions of homogeneous algebraic Diophantine diagonal equations with integer coefficients" @default.
- W4293482216 doi "https://doi.org/10.48550/arxiv.1604.07646" @default.
- W4293482216 hasPublicationYear "2016" @default.
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