Higher order divisor functions over values of mixed powers

2024/04/21 by Du, Chenhao, Sun, Qingfeng
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2404.13666

Abstract

Let τ_k(n) be the k-th divisor function. In this paper, we derive an asymptotic formula for the sum ∑_1≤ n₁,n₂, …, n_ℓ≤ X^(1)/(r) \atop 1≤ n_ℓ+1≤ X^(1)/(s)τ_k(n₁^r+n₂^r+… +n_ℓ^r+n_ℓ+1^s), where k≥ 4, r≥ 2, s≥ 2 and ℓ≥ 2 are integers. Previously only special cases are studied.

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