Sums of the triple divisor function over values of a ternary quadratic form

2015/10/21 by Sun, Qingfeng, Zhang, Deyu
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1510.06170

Abstract

Let τ₃(n) be the triple divisor function which is the number of solutions of the equation d₁d₂d₃=n in natural numbers. It is shown that ∑_{1≤ n1,n2,n3≤ √(x)}τ₃(n₁²+n₂²+n₃²)=c₁x^(3)/(2)(log x)²+ c₂x^(3)/(2)log x +c₃x^(3)/(2) +O_ε(x^(11)/(8)+ε) for some constants c₁, c₂ and c₃.

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• Sum of the triple divisor function and Fourier coefficients of SL(3,ℤ) Hecke-Maass forms over quadratics
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