Determination of the asymptotic behavior of the number of natural solutions for certain types of diagonal Diophantine equations

2020/01/22 by Volfson, Victor
#11D45 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2001.07936

Abstract

We obtain asymptotic upper bounds for the number of natural solutions of the following diagonal Diophantine equations in a hypercube with side - N in the paper: x₁ = x₂^k+...+x_s^k, x₁^k = x₂^k+...+x_s^k, x₁ = ∑_j=2^s x_j^k_j, where k,s,k_j are the natural numbers.

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