On high power moments of the error term of the Dirichlet divisor function over primes

2024/10/01 by Zhen Guo, Xin Li, Guo, Zhen +1
Mathematics · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2410.00936

openalex publication_date 2024/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let 3\leqslant k\leqslant9 be a fixed integer, p be a prime and d(n) denote the Dirichlet divisor function. We use Δ(x) to denote the error term in the asymptotic formula of the summatory function of d(n). The aim of this paper is to study the k-th power moments of Δ(p), namely ∑_{p\leqslant x}Δ^k(p), and we give an asymptotic formula.

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