On the Seventh Power Moment of Δ(x)

2016/01/21 by Jinjiang Li, Li, Jinjiang
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1601.05515

openalex publication_date 2016/01/21 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Let Δ(x) be the error term of the Dirichlet divisor problem. In this paper, we establish an asymptotic formula of the seventh-power moment of Δ(x) and prove that ∫₂^T Δ⁷(x)dx= \frac7(5s_7;3(d)-3s_7;2(d)-s_7;1(d))2816π⁷T^11/4+O(T^{11/4-δ₇+ε}) with δ₇=1/336, which improves the previous result.

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